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\MBRIDGE   PHYSICAL   SERIES. 


CONDUCTION  OF  ELECTRICITY 
THROUGH  GASES 


1 


EonDon:   C.  J.   CLAY   AND   SONS, 

CAMBRIDGE    UNIVERSITY  PRESS  WAREHOUSE, 

AVE   MARIA  LANE. 

AND 

H.   K.   LEWIS, 
136,   GOWER   STREET,   W.C. 


(Slaaaoto:   50,  WELLINGTON  STREET. 

Ettpjig:    F.  A.  BROCKHAUS. 

#rfo  Hork:    THE  MACMILLAN  COMPANY. 

Bombay  anH  Calcutta:    MACMILLAN  AND  CO.,  LTD. 


[All  Rights  reserved.] 


ONDUCTION  OF  ELECTEICITY 
THROUGH  GASES         J 


BY 


J.   J.   THOMSON,   D.Sc.,  LL.D.,   PH.D.,  F.R.S. 

FELLOW  OF  TRINITY  COLLEGE,  CAMBRIDGE 
CAVENDISH  PROFESSOR  OF  EXPERIMENTAL  PHYSICS,  CAMBRIDGE 


CAMBRIDGE : 

AT   THE   UNIVERSITY   PRESS. 
1903 


Oc  711 

'  T4- 


Cambridge : 

PRINTED   BY  J.    AND   C.    F.   CLAY, 
AT    THE    UNIVERSITY   PRESS. 


I 

Si 

if  PREFACE. 


T  HAVE  endeavoured  in  this  work  to  develope  the  view  that 
-  the  conduction  of  electricity  through  gases  is  due  to  the 
presence  in  the  gas  of  small  particles  charged  with  electricity, 
called  ions,  which  under  the  influence  of  electric  forces  move 
from  one  part  of  the  gas  to  another.  My  object  has  been  to 
show  how  the  various  .phenomena  exhibited  when  electricity 
passes  through  gases  can  be  coordinated  by  this  conception 
rather  than  to  attempt  to  give  a  complete  account  of  the  very 
numerous  investigations  which  have  been  made  on  the  electrical 
properties  of  gases ;  I  have  therefore  confined  myself  for  the 
most  part  to  those  phenomena  which  furnish  results  sufficiently 
precise  to  serve  as  a  test  of  the  truth  of  this  theory.  The  book 
contains  the  subject-matter  of  lectures  given  at  the  Cavendish 
Laboratory  where  a  good  deal  of  attention  has  been  paid  to 
the  subject  and  where  a  considerable  number  of  physicists  are 
working  at  it. 

The  study  of  the  electrical  properties  of  gases  seems  to  offer 
the  most  promising  field  for  investigating  the  Nature  of  Electricity 
and  the  Constitution  of  Matter,  for  thanks  to  the  Kinetic  Theory 
of  Gases  our  conceptions  of  the  processes  other  than  electrical 
which  occur  in  gases  are  much  more  vivid  and  definite  than  they 
are  for  liquids  or  solids;  in  consequence  of  this  the  subject  has 
advanced  very  rapidly  and  I  think  it  may  now  fairly  be  cla:  ned 
that  our  knowledge  of  and  insight  into  the  processes  going  on 
when  electricity  passes  through  a  gas  is  greater  than  it  is  in 
the  case  either  of  solids  or  liquid.  The  possession  of  a  charge 
by  the  ions  increases  so  much  the  ease  with  which  they  can  be 
traced  and  their  properties  studied  that  as  the  reader  will  see 
we  know  far  more  about  the  ion  than  we  do  about  the  uncharged 
molecule. 


vi  PREFACE. 


L 


With  the  discovery  and  study  of  Cathode  rays,  Rb'ntgen  rays 
and  Radio-activity  a  new  era  has  begun  in  Physics,  in  which  the 
electrical -properties  of  gases  have  played  and  will  play  a  most 
important  part ;  the  bearing  of  these  discoveries  on  the  problems 
of  the  Constitution  of  Matter  and  the  Nature  of  Electricity  is  in 
most  intimate  connection  with  the  view  we  take  of  the  processes 
which  go  on  when  electricity  passes  through  a  gas.  I  have 
endeavoured  to  show  that  the  view  taken  in  this  volume  is 
supported  by  a  large  amount  of  direct  evidence  and  that  it 
affords  a  direct  and  simple  'explanation  of  the  electrical  properties 
of  gases. 

The  pressure  of  my  other  duties  has  caused  this  book  to  be 
a  considerable  time  in  passing  through  the  press,  and  some 
important  investigations  have  been  published  since  the  sheets 
relating  to  the  subjects  investigated  were  struck  off.  I  have 
given  a  short  account  of  these  in  a  few  Supplementary  Notes. 

My  thanks  are  due  to  Mr  C.  T,  R.  Wilson,  F.R.S.,  for  the 
'assistance  he  has  given  me  by  reading  the  proofs  and  I  am 
indebted  to  Mr  Hayles  of  the  Cavendish  Laboratory  for  the 
preparation  of  the  diagrams. 

J.  J.  THOMSON. 


CAVENDISH  LABORATORY,  CAMBRIDGE. 
August,  1903. 


TABLE   OF  CONTENTS. 


CHAP.  PAOB 

I.  Electrical  Conductivity  of  Gases  in  a  normal  state     .  C  1 

II.  Properties  of  a  Gas  when  in  the  conducting  state       .        .  8 

III.  Mathematical  Theory  of  the  Conduction  of  Electricity  through 

a  Gas  containing  Ions .  64 

IV.  Effect  produced  by  a  Magnetic  Field  on  the  Motion  of  the 

Ions  .         .         .         .        .        .        .'»;*•.        .  79 

V.      --Determination  of  the  Ratio  of  the  Charge  to  the  Mass  of 

an  Ion  91 


VI.        Determination  of  the  Charge  carried  by  the  Negative  Ion  .      121 

VII.  On  some  Physical  Properties  of  Gaseous  Ions      .        .        .      133 

VIII.  lonisation  by  Incandescent  Solids          ,\     T^V.        .        •       155 

IX.  lonisation  in  Gases  from  Flames  .  -^^\     \,        .        .        .       193 

X.  •  lonisation  by  Light.     Photo-Electric  Effects         .        .        .211 
XL        lonisation  by  Rontgen  Rays.        .        .        .    \.        .        .      244 
XII.       Becquerel  Rays       .      \        .        *       .,.'.''.      \        .        .      274 

l/XIIL  •    Spark^Discharge    c^/   \      .     .'.        .      ,,        .        .        .      346 

XIV.      The_Electric  Arc     .    .  *  ,,  \  .        .        •        •        •        •        •      416 

v  XV.       Discjarge  through  Gases  at  Low  Pressures  .  ^  .     '    .        .      432 

XVI.  Theory  of  the  Discharge  through  Vacuum  Tubes    .     .        .479 

XVII.  Qailiode  Rays         '.        .  493 

XVIII.  Rontgen  Rays          . 523 

XIX.      Properties  of  Moving  Electrified  Bodies        ....      530 

SUPPLEMENTARY  NOTES .545 

INDEX  555 


CHAPTER  I. 

ELECTRICAL  CONDUCTIVITY  OF  GASES  IN  A  NORMAL  STATE. 

1.  A  GAS  in  the  normal  state  conducts  electricity  to  a  slight, 
but  only  to  a  very  slight,  extent,  however  smallythe  electric  force 
acting  on  the  gas  may  be.     So  small  however  is  the  conductivity 
of  a  gas  when  in  this  state,  and  so  difficult  is  it  to  eliminate 
spurious  effects,  that  there  have  been  several  changes  of  opinion 
among  physicists  as  to  the  cause  of  the  leakage  of  electricity  which 
undoubtedly  occurs  when  a  charged  body  is  surrounded  by  gas.   It 
was  thought  at  first  that  this  leakage  took  place  through  the  gas ; 
later,  as  the  result  of  further  experiments,  it  was  attributed  to 
defective  insulation  of  the  rods  or  threads  used  to  support  the 
body,  and  to  the  dust  present  in  the  gas ;  quite  recently  however 
it  has  been  shown  that  there  is  a  true  leak   through  the  gas 
which  is  not  due  to  the  dust  or  moisture  the  gas  may  happen 
to  contain. 

2.  The  escape  of  electricity  from  an  insulated  charged  body 
has  attracted  the  attention  of  many  physicists.    Coulomb*,  whose 
experiments  were  published  in  1785,  from  his  investigations  on 
the  loss  of  electricity  from  a  charged  body  suspended  by  insulat- 
ing strings,  came   to  the  conclusion  that  after  allowing  for  the 
leakage  along  the  strings  there  was  a  balance  over,  which  he 
attributed  to  a  leakage  through  the  air.    He  explained  this  leakage 
by  supposing  that  the  molecules  of  air  when  they  come  into  con- 
tact  with  a  charged  body  receive  a  charge  of  electricity  of  the 
same    sign    as   that  on  the  body  and  are  then  repelled  from  it 
carrying  off  some  of  the  charge.     We  shall  see  later  on  that  this 
explanation  is  not  tenable. 

*  Coulomb   Memoires  de  VAcademie  des  Sciences,  1785,  p.  612. 

1 


2  ELECTRICAL   CONDUCTIVITY  [2 

Matteucci*  experimenting  on  the  same  subject  in  1850  also 
came  to  the  conclusion  that  there  was  a  leakage  of  electricity 
through  the  gas ;  he  was  the  first  to  prove  that  the  rate  at  which 
this  leak  takes  place  is  less  when  the  pressure  of  the  gas  is  low 
than  when  it  is  high.  He  found  also  that  the  rate  of  leak  was 
the  same  in  air,  carbonic  acid  and  hydrogen.  On  the  other  hand 
Warburg f  found  that  the  rate  of  leak  through  hydrogen  was  only 
about  half  of  that  through  air  and  carbonic  acid,  he  agreed  with 
Matteucci  with  regard  to  the  equality  of  the  rate  of  leak  through 
the  other  two  gases  arid  could  detect  no  difference  between  the 
leaks  through  dry  and  moist  air ;  he  confirmed  Matteucci's  obser- 
vations on  the  effect  of  pressure  on  the  rate  of  leak.  Warburg 
seemed  inclined  to  suspect  that  the  leak  was  due  to  dust  in  the 
gases.  The  belief  in  dust  being  the  carrier  of  the  electricity  was 
strengthened  by  an  experiment  made  by  Hittorf  J  in  which  a  small 
carefully  insulated  gold  leaf  electroscope  was  placed  in  a  glass 
vessel  filled  with  filtered  gas ;  the  electroscope  was  found  to  have 
retained  a  charge  even  after  the  lapse  of  four  days.  We  know 
now  from  recent  experiments  that  the  smallness  of  the  leak 
observed  in  this  case  was  due  to  the  smallness  of  the  vessel 
in  which  the  charged  body  was  placed  rather  than  to  the  absence 
of  dust. 

Further  experiments  on  this  subject  were  made  by  Nahrwold§ 
and  by  Narr||  who  showed  that  the  rate  of  leak  from  a  charged 
hollow  sphere  was  not  increased  when  the  temperature  of  the 
sphere  was  raised  by  filling  it  with  hot  water.  BoysH  made  an 
experiment  which  showed  very  clearly,  that  whatever  the  cause  of 
the  leak  might  be,  it  was  not  wholly  due  to  want  of  insulation  in 
the  supports  of  the  charged  body;  in  this  experiment  he  attached 
the  gold  leaves  of  an  electroscope  first  to  a  short  and  thick  quartz 
rod  and  then  to  a  long  and  thin  one,  and  found  that  the  rate  of 
leak  of  electricity  from  the  gold  leaves  was  the  same  in  the  two 
cases;  if  the  leak  had  been  along  the  supports  it  would  have 

*  Matteucci,  Annales  de  Chimie  et  de  Physique,  xxviii.  p.  390,  1850. 
t  Warburg,  Pogg.  Ann.  cxlv.  p.  578,  1872. 
£  Hittorf,  Wied.  Ann.  vii.  p.  595,  1879. 
§  Nahrwold,  Wied.  Ann.  v.  p.  460,  1878 ;  xxxi.  p.  448,  1887. 
||  Narr,  Wied.  Ann.  v.  p.  145,  1878;  viii.  p.  266,  1879;  xi.  p.  155,  1880;  xvi.. 
p.  558,  1882;  xxii.  p.  550,  1884;  xliv.  p.  133,  1892. 
IT  Boys,  Phil.  Mag.  xxviii.  p.  14,  1889. 


OF   GASES  IN  A  NORMAL  STATE. 


a 


been  much  greater  in  the  first  case  than  in  the  second.  Boys 
also  confirmed  Warburg's  observation  that  the  rate  of  leak  was 
the  same  in  dry  and  moist  air. 

3.  The  subject  of  the  electric  conduction  through  air  is 
evidently  of  considerable  importance  in  relation  to  Meteorology 
and  Atmospheric  Electricity.  Experiments  especially  bearing  on 
this  point,  were  made  by  Linss*  on  the  loss  of  electricity  from 
charged  bodies  placed  in  the  open  air;  he  found  tbe^vas  an 
appreciable  loss  of  charge  which  control  experiments  *|pc<l  was 
not  due  to  leakage  along  the  supports  of  the  charged  body. 

An  extensive  series  of  open  air  measurements  were  made  by 
Elster  and  Geitelf  in  many  different  localities  and  in  different 
states  of  the  weather.  They  found  that  the  rate  of  leak  varied 
from  time  to  time  and  from  place  to  place,  that  it  was  very 
smaller  in  mist  or  fog  than  when  the  weather  was  bright 
and  clear,  that  it  was  greater  at  high  altitudes  than  at  low  ones, 
and  that  on  the  tops  of  mountains  the  rate  of  escape  of  negative 
electricity  was  much  greater  than  that  of  positive.  This  is  doubt- 
less due  to  the  negative  charge  on  the  earth's  surface,  a  mountain 
top  being  analogous  to  a  sharp  point  on  a  conductor  and  thus  a 
place  where  the  earth's  electric  force  is  much  greater  than  it  is  on 
the  plains,  where  they  found  the  rate  of  leak  to  be  the  same 
for  plus  and  minus  charges.  These  points  are  brought  out  by  the 
results  of  the  observations  given  in  Tables  I.  and  II.  Table  I. 
gives  the  results  of  experiments  made  at  Wolfenbiittel  at  different 
times.  Table  II.  contains  observations  at  different  places. 

TABLE  I. 


Weather 

Bate  of  leak 
for  +  charge 

Bate  of  leak 
for  -  charge 

Fog,  wind  S.E  ,  

277 

2-64 

Clear,  air  very  transparent             

8-58 

9-82 

Fine  rain,  mist  ...         

318 

3-02 

Sky  half  overcast,  air  very  transparent... 

13-67 

13-83 

*  Linss,  MeteoroL  Zeitschr.  iv.  p.  352,  1887;   Elektrotechn.  Zeitschr.  i.   11, 
p.  506,  1890. 

t  Elster  and  Geitel,  Drudes  Ann.  ii.  p.  425,  1900. 

1—2 


ELECTRICAL  CONDUCTIVITY 


[4 


TABLE  II. 


Place  and  altitude 

Weather 

Kate  of  leak 
+  charge 

Rate  of  leak 
-  charge 

Brocken,      1140m. 

Sunshine,  hazy 

6-67 

10'28 

Weissbad           .     800  m. 

Sunshine,  air  clear 

9-66 

9-52 

Santisgipfel,    ...  2500m. 
Gornergrat,  3140  m. 
Zermatt  Valley,  1620  m. 
Wolfenbuttel,  ...       80  m. 

Sunshine,  air  very  clear 
Sunshine,  air  very  clear 
Sunshine 
No  clouds,  air  clear 

8-95 
3-28 
21-02 
8-45 

35-04 
31-26 

20-78 
9-20 

4.  Further  experiments  on  the  rates  of  leak  from  a  charged 
body  placed  in  a  closed  vessel  filled  with  air  were  made  almost 
simultaneously  by  Geitel*  and  by  Wilson f.  The  apparatus  used 
by  Wilson  for  this  purpose  is  represented  in  Fig.  1.  Since  the 


Fig.  1. 

quantity  of  electricity  which  escapes  from  the  charged  body  is 
very  small  it  is  necessary  that  the  capacity  of  the  instrument  used 
to  measure  it  should  be  small ;  this  condition  makes  it  advisable 
to  use  a  small  gold  leaf  electroscope  rather  than  a  quadrant 
electrometer.  To  prevent  the  leakage  from  the  supports  vitiating 
the  experiments  the  brass  strip  which  carries  the  gold  leaf  is 
attached  to  and  insulated  from  a  metal  rod  A  by  a  piece  of 

*  Geitel,  Physikalische  Zeitschr.  ii.  p.  116,  1900. 

t  Wilson,  Proc.  Camb.  Phil.  Soc.  xi.  p.  32,  1900 ;  Proc.  Roy.  Soc.  Ixviii.  p.  151, 
1901. 


4]  OF   GASES   IN   A   NORMAL  STATE.  5 

sulphur  B,  A  being  insulated  by  a  plug  of  sulphur  from  the  vessel 
containing  the  gas  under  examination,  and  connected  with  a 
condenser  C  formed  of  parallel  plates  of  metal  imbedded  in  a 
block  of  sulphur.  The  brass  strip  and  gold  leaf  are  initially 
charged  to  the  same  potential  as  the  rod  by  making  momentary 
contact  between  the  rod  and  the  strip ;  the  rod  being  connected 
with  a  large  capacity  remains  at  almost  constant  potential,  and 
thus  if  there  is  any  leakage  of  electricity  along  the  sulphur 
supporting  the  brass  strip  and  gold  leaf,  it  will  tend  to  keep  them 
charged  and  not  to  discharge  them.  The  position  of  the  gold  leaf 
was  read  by  means  of  a  microscope  provided  with  an  eye-piece 
micrometer  scale.  The  brass  strip  and  gold  leaf  were  used  as  the 
charged  body  and  the  rate  at  which  the  image  of  the  gold  leaf 
moved  across  the  micrometer  scale  was  a  measure  of  the  rate  of 
leak  through  the  gas.  The  following  results  were  obtained  by 
both  Geitel  and  Wilson — the  rate  of  escape  of  electricity  in  a 
closed  vessel  is  much  smaller  than  in  the  open  and  the  larger  the 
vessel  the  greater  is  the  rate  of  leak.  The  rate  of  leak  does  not 
increase  in  proportion  to  the  difference  of  potential  between  the 
gold  leaves  and  the  walls  of  the  vessel ;  the  rate  soon  reaches 
a  limit*'  beyond  which  it  does  not  increase  however  much  the 
potential  difference  is  increased  (provided  of  course  that  this  is 
not  great  enough  to  cause  sparks  to  pass). 

It  follows  from  Wilson's  experiments  that  in  dust-free  air  at 
atmospheric  pressure  the  maximum  quantity  of  electricity  which 
can  escape  in  one  second  from  a  charged  body  in  a  closed  space 
whose  volume  is  V  cubic  centimetres  is  about  10~8  V  electrostatic 
units.  Rutherford  and  Allen*  working  in  Montreal  obtained 
results  in  close  agreement  with  this. 

As  the  result  of  a  series  of  experiments  made  at  pressures 
ranging  from  43  to  743  millimetres  of  mercury  Wilson  came  to 
the  conclusion  that  the  maximum  rate  of  leak  is  very  approximately 
proportional  to  the  pressure,  thus  at  low  pressures  the  rate  of  leak 
is  exceedingly  small :  this  result  is  illustrated  in  a  striking  way  by 
an  observation  of  Crookesf  that  a  pair  of  gold  leaves  could  retain 
an  electric  charge  for  months  in  a  very  high  vacuum.  The  rate  of 
leak  is  about  the  same  in  the  dark  as  it  is  in  the  light,  it  is  thus 

*  Rutherford  and  Allen,  Physikalische  Zeitschr.  Hi.  p.  225,  1902. 
t  Crookes,  Proc.  Roy.  Soc.  xxviii.  p.  347,  1879. 


6  ELECTRICAL  CONDUCTIVITY  [5 

not  due  to  light,  and  that  it  can  be  caused  by  some  invisible  form 
of  radiation  is  rendered  improbable  by  the  observation  of  Wilson 
that  the  rate  of  leak  in  a  closed  vessel  is  the  same  when  the  vessel 
is  inside  a  railway  tunnel  as  when  it  is  outside  ;  in  the  former  case 
any  radiation  reaching  the  gas  from  outside  must  have  travelled 
through  many  feet  of  solid  rock.  Wilson*  has  recently  investigated 
the  greatest  rates  of  leak  through  different  gases  and  has  obtained 
the  following  results. 

Relative  rate  of  leak 
Gas  Relative  rate  of  leak  Specific  gravity 

air  1-00  I'OO 

Ho  -184  2'7 

C02  1-69  1-10 

S02  2-64  1-21 

CHC13  4-7  1-09 

5.  Geitel  (loc.  cit.)  made  the  very  interesting  observation  that 
the  rate  of  leak  in  a  closed  vessel  increases,  after  the  refilling  of 
the  vessel  with  fresh  air,  for  some  days,  when  it  reaches  a  constant 
value  at  which  it  remains  for  an  indefinitely  long  time.  The  most 
obvious  explanation  of  this  result  is  that  it  is  due  to  the  settling 
down  of  the  dust,  as  Elster  and  Geitel  (loc.  cit)  have  shown  that 
the  presence  of  dust,  fog,  or  mist  diminishes  the  rate  of  leak.  This 
explanation  is  however  rendered  doubtful  by  some  later  experi- 
ments f  made  by  the  same  physicists,  in  which  they  found  that 
the  period  required  for  the  gas  to  attain  its  maximum  conduc- 
tivity was  not  appreciably  diminished  by  filtering  the  dust  out  of 
the  air  by  sending  it  through  water,  or  by  extracting  the  moisture 
from  the  gas :  thus  if  the  increase  in  the  rate  of  leak  is  due  to  the 
settling  down  of  some  foreign  matter  from  the  gas,  this  matter 
must  be  something  which  can  not  be  got  rid  of  by  filtering  the 
gas  through  water  traps  or  plugs  of  glass-wool :  we  shall  find  later 
on  when  we  study  the  diselectrification  of  ga,ses  that  there  are 
cases  in  which  foreign  matter  present  in  gases  is  not  removed  by 
such  treatment,  and  the  case  of  the  discharge  of  negative  elec- 
tricity from  a  point  (vide  infra)  shows  that  under  certain  con- 
ditions the  admixture  of  a  very  small  amount  of  foreign  matter  to 
a  gas  produces  a  great  diminution  in  the  rate  of  escape  of  electri- 
city through  it.  ft 

*  Wilson,  Proc.  Roy.  Soc.  Ixix.  p.  277,  1901. 

t  Elster  and  Geitel,  Physikalische  Zeitschr.  ii.  p.  560,  1901. 


6]  OF   GASES   IN  ,A   NORMAL  STATE.  7 

6.  Another  aspect  of  this  phenomenon  is  the  very  interesting 
fact  discovered  by  Elster  and  Geitel*  that  the  rate  of  leak  in 
caves,  and  cellars  where  the  air  is  stagnant  and  only  renewed 
slowly,  is  very  much  greater  than  in  the  open  air  :  thus  in  some 
experiments  they  made  in  a  cave— the  Baumannshohle  in  the  Harz 
Mountains — they  found  that  in  the  cave  the  electricity  escaped  at 
seven  times  the  rate  it  did  in  the  air  outside  even  when  this  was 
clear  and  free  from  mist.  They  found  too  that  in  a  cellar  whose 
windows  had  been  shut  for  eight  days  the  rate  of  leak  was  very 
considerably  greater  than  it  was  in  the  air  outside.  These  experi- 
ments suggest  that  gas  having  abnormally  great  conductivity 
slowly  diffuses  from  the  walls  surrounding  the  gas,  and  that  this 
diffusion  goes  on  so  slowly  that  when  fresh  gas  is  introduced  it 
takes  a  considerable  time  for  the  gas  from  the  walls  to  again 
diffuse  through  the  volume.  The  reader  should  compare  with 
this  phenomenon  the  results  described  in  the  Chapter  on  Induced 
Radioactivity. 

The  experiments  we  have  described  show  that  the  rate  of 
leak  of  electricity  through  gas  in  a  normal  state  is  influenced  by 
a  great  variety  of  circumstances,  such  as  the  pressure  of  the  gas, 
the  volume  of  gas  in  the  electric  field,  and  the  amount  of  dust  or 
fog  held  in  suspension  by  it;  all  these  effects  receive  a  ready 
explanation  on  the  view  to  which  we  are  led  by  the  study  of  the 
effects  shown  on  a  larger  scale  by  gases  whose  conductivity  has 
been  increased  by  artificial  means,  and  we  shall  return  to  the 
subject  of  the  leak  through  normal  air  after  the  study  of  gases 
whose  conductivity  has  been  abnormally  increased.  We  may 
however  at  once  point  out  that  the  increase  of  the  rate  of  leak 
with  the  size  of  the  vessel  containing  the  charged  body  shows  that 
the  conduction  is  not  due,  as  Coulomb  thought,  to  particles  of  gas 
originally  uncharged  striking  against  the  charged  body  and 
receiving  a  charge  which  they  deliver  up  to  the  sides  of  the  vessel ; 
if  this  were  the  method  by  which  the  electricity  escaped  the  rate 
of  leak  would  not  increase  with  the  size  of  the  vessel. 

*  Elster  and  Geitel,  Physikalische  Zeitschr.  ii.  p.  560,  1901. 


CHAPTER  II. 

PROPERTIES  OF   A  GAS  WHEN  IN  THE  CONDUCTING  STATE. 

7.  THE  electrical  conductivity  of  gases  in  the  normal  state  is 
so  small  that  as  we  have  seen  the  proof  of  its  existence  requires 
very  careful  and  elaborate  experiments.     Gases  may  however  in 
various  ways  be  put  into  a  state  in  which  they  conduct  electricity 
with  so  much  facility  that  the  detection  and  investigation  of  this 
property  becomes  a  comparatively  easy  matter ;  as  the  study  of 
the  properties  of  a   gas   when   in  this  state   is   of  the   highest 
importance  from  the  light  which  it  throws  on  the  general  phe- 
nomena of  electric  discharge  through  gases  we  shall  find  it  useful 
to  discuss  the  subject  at  some  considerable  length. 

8.  There  are  many  ways  in  which  gases  may  be  made  to 
possess  considerable  conductivity  or,  as  we  shall  express  it,  be  put 
into  the  conducting  state.     They  are  for  instance  put  into  this 
state  when  their  temperature  is  raised  above  a  certain  point ;  again, 
gases  drawn  from  the  neighbourhood  of  flames  or  electric  arcs  or 
which  have  recently  been  in  contact  with  glowing  metals  or  carbon, 
or  have  diffused  from  a  space  through  which  an  electric  discharge 
is  passing  or  has  recently  passed,  are  in  this  state.     A  gas  is  put 
into  the  conducting  state  when  Rontgen,  Lenard  or  Cathode  rays 
pass  through  it,  the  same  effect  is  produced  by  the  rays  from 
uranium,  thorium,  or  the  radioactive  substances,  polonium,  radium, 
actinium,  obtained  from  pitch-blende  by  Curie,  Curie  and  Bemont 
and  Debierne  respectively,  and  also  as  Lenard  has  recently  shown 
by  a  very  easily  absorbed  kind  of  ultra-violet  light.     E.  Wiede- 
mann  has  shown  that  electric  sparks  give  out  rays,  called  by  him 
Entladungstrahlen,  which  produce  the  same  effect.    Air  which  has 
passed  over  phosphorus   or  which   has   bubbled    through    water 
is  also  in  this  state  and  remains  so  for  some  time  after  it  has 


9]      PROPERTIES   OF   A   GAS   WHEN  IN   THE   CONDUCTING  STATE.      9 

left  the  phosphorus  or  water.  We  shall  have  later  on  to  discuss 
the  action  of  each  of  these  agents  in  detail,  but  we  shall  begin  by 
studying  some  of  the  general  properties  possessed  by  a  gas  when 
in  this  state,  the  experimental  methods  by  which  these  properties 
may  be  investigated,  and  a  theory  of  this  state  by  which  they  may 
be  explained. 

9.  A  gas  when  in  the  conducting  state  possesses  characteristic 
properties.  In  the  first  place  it  retains  its  conductivity  for  some 
little  time  after  the  agent  which  made  it  a  conductor  has  ceased 
to  act ;  its  conductivity  however  always  diminishes,  in  some  cases 
very  rapidly,  after  the  agent  is  removed,  and  finally  it  disappears. 
The  duration  of  the  conductivity  may  be  shown  very  simply  by 
having  a  charged  electroscope  screened  off  from  the  direct  action 
of  Rontgen  rays,  the  electrostatic  field  due  to  the  electroscope 
being  screened  off  from  the  region  exposed  to  the  rays  by  covering 
the  electroscope  with  a  cage  made  of  wire  gauze  with  a  very  large 
mesh  ;  if  the  air  is  still  the  electroscope  will  retain  its  charge  even 
when  the  rays  are  in  action,  but  if  we  blow  some  of  the  air 
traversed  by  the  rays  towards  the  electroscope  the  latter  will 
begin  to  lose  its  charge,  showing  that  the  air  has  retained  its  con- 
ductivity for  the  time  taken  by  it  to  travel  to  the  electroscope 
from  the  place  where  it  was  exposed  to  the  rays.  A  somewhat  more 
elaborate  form  of  this  experiment,  which  enables  us  to  prove  several 
other  interesting  properties  of  the  conducting  gas,  is  to  place  the 
electroscope  in  a  glass  vessel  A  in  which  there  are  two  tubes,  one 
leading  to  a  water-pump  while  the  end  of  the  other  is  in  the  region 
traversed  by  the  Rontgen  rays.  The  tube  used  to  produce  the  rays 


c 


Fig.  2. 

is  placed  in  a  box  covered  with  lead  with  the  exception  of  a 
window  at  B  to  let  the  rays  through  :  this  shields  the  electroscope 


10  PROPERTIES   OF  (^GASjJ  [10 

from  the  direct  action  of  the  rays :  if  the  water-pump  be  worked 
slowly  so  as  to  make  a  slow  current  of  air  pass  from  the  region 
traversed  by  the  rays  into  the  vessel  A  the  electroscope  will 
gradually  lose  its  charge  whether  this  be  positive  or  negative :  if 
the  pump  be  stopped  and  the  current  of  air  ceases,  the  discharge 
of  the  electroscope  will  cease. 

The  conducting  gas  loses  its  conductivity  if  it  is  sucked  through 
a  plug  of  glass-wool  or  made  to  bubble  through  water*.  This  can 
readily  be  proved  by  inserting  in  the  tube  B  a  plug  of  glass-wool 
or  a  water-trap  and  working  the  water-pump  a  little  harder  so  as 
to  make  the  rate  of  flow  of  air  through  the  tube  the  same  as  in 
the  previous  experiment ;  it  will  now  be  found  that  the  electroscope 
will  retain  its  charge,  the  conductivity  has  thus  been  taken  out  of 
the  gas  by  filtering  it  through  glass-wool  or  water.  The  con- 
ductivity is  very  much  more  easily  removed  from  gases  made 
conducting  by  the  various  rays,  Rontgen,  Lenard,  Cathode,  &c., 
than  from  the  conducting  gases  derived  from  flames  and  arcs ;  the 
latter  as  we  shall  see  require  a  great  deal  of  filtering  to  remove 
their  conductivity.  If  we  replace  the  tube  B  by  a  metal  tube  of 
fine  bore  we  shall  find  that  the  gas  loses  its  conductivity  by  passing 
through  it,  and  the  finer  the  bore  the  more  rapidly  does  the  con- 
ductivity disappear.  The  conductivity  may  also  be  removed  from 
the  gas  by  making  it  traverse  a  strong  electric  field  so  that  a 
current  of  electricity  passes  through  itf.  To  show  this,  replace 
the  glass  tube  C  by  a  metal  tube  of  fairly  wide  bore  and  fix  along 
the  axis  of  this  tube  an  insulated  metal  wire;  if  there  is  no 
potential  difference  between  the  wire  and  the  tube,  then  the 
electroscope  in  A  will  leak  when  a  current  of  air  is  sucked  through 
the  apparatus ;  if  however  a  considerable  difference  of  potential  is 
established  between  the  wire  and  the  tube,  so  that  a  current  of 
electricity  passes  through  the  gas  during  its  passage  to  A,  the 
leak  of  the  electroscope  will  cease,  showing  that  the  conductivity 
of  the  gas  has  been  removed  by  the  electric  field. 

10.  The  removal  of  the  conductivity  by  filtering  through 
glass-wool  or  water  and  by  transmission  through  narrow  metal 
tubes,  shows  that  the  conductivity  is  due  to  something  mixed 

*  J.  J.  Thomson  and  E.  Rutherford,  Phil.  Mag.  xlii.  p.  392,  1896. 
t  Ibid. 


11] 


WHEN   IN   THE  CONDUCTING   STATE. 


11 


with  the  gas,  this  something  being  removed  from  the  gas  in  the 
one  case  by  filtration  in  the  other  by  diffusion  to  the  walls  of  the 
tube.  Further  the  removal  of  the  conductivity  by  the  electric 
field  shows  that  this  something  is  charged  with  electricity  and 
moves  under  the  action  of  the  field ;  since  the  gas  when  in  the 
conducting  state  shows  as  a  whole  no  charge  of  electricity,  the 
charges  removed  must  be  both  positive  and  negative.  We  are 
thus  led  to  the  conclusion  that  the  conductivity  of  the  gas  is  due 
to  its  having  mixed  with  it  electrified  particles,  some  of  these 
particles  having  charges  of  positive  electricity  others  of  negative. 
We  shall  call  these  electrified  particles  ions,  and  the  process  by 
which  a  gas  is  made  into  a  conductor  the  ionisation  of  the  gas. 
We  shall  show  later  on  how  the  masses  and  charges  of  the  ions 
may  be  determined,  when  it  will  appear  that  the  ions  in  a  gas  are 
not  identical  with  those  met  with  in  the  electrolysis  of  solutions. 

11.  The  passage  of  a  current  of  electricity  through  a  conducting 
gas  does  not  follow  Ohm's  law  unless  the  electromotive  force  acting 
on  the  gas  is  small.  We  may  investigate  the  relation  between  the 
current  and  potential  difference  by  taking  two  parallel  metal 
plates  A  and  B  (Fig.  3)  immersed  in  a  gas,  the  gas  between  the 


•it  hi 


forth 


Fig.  3. 


plates  being  exposed  to  the  action  of  some  ionising  agent  such  as 
Rontgen  rays  or  the  radiation  from  a  radioactive  substance.  One 
of  the  plates  A  is  connected  with  one  of  the  pairs  of  quadrants  of 
an  electrometer,  the  other  pair  of  quadrants  being  put  to  earth. 
The  other  plate  B  is  connected  with  one  of  the  terminals  of  a 


12 


PROPERTIES  OF  A  GAS 


[11 


battery  of  several  storage  cells,  the  other  terminal  of  the  battery 
being  connected  with  the  earth  ;  initially  the  two  pairs  of  quad- 
rants of  the  electrometer  are  connected  together,  then  the  con- 
nection between  the  quadrants  is  broken  and  as  a  current  of 
electricity  is  passing  across  the  air  space  between  A  and  B,  the 
plate  B  gets  charged  up  and  the  needle  of  the  electrometer  is 
deflected ;  the  rate  of  deflection  of  the  electrometer  measures  the 
current  passing  through  the  gas.  By  making  a  series  of  obser- 
vations of  this  kind  we  can  get  the  means  of  drawing  a  curve  such 
that  the  ordinates  represent  the  current  through  the  gas  and  the 
abscissae  the  potential  difference  between  the  plates :  such  a  curve 
is  represented  in  Fig.  4*.  We  see  that  when  the  difference  of 


Fig.  4. 


potential  is  small  the  curve  is  a  straight  line,  in  this  stage  the 
conduction  obeys  Ohm's  law ;  the  current  however  soon  begins  to 
increase  more  slowly  than  the  potential  difference  and  we  reach  a 
stage  where  there  is  no  appreciable  increase  of  current  when  the 
potential  difference  is  increased :  in  this  stage  the  current  is  said 
to  be  saturated.  When  the  potential  difference  is  increased  to 
such  an  extent  that  the  electric  field  is  strong  enough  to  ionise 
the  gas,  another  stage  is  reached  in  which  the  current  increases 
very  rapidly  with  the  potential  difference;  curves  showing  this 
effect  have  been  obtained  by  von  Schweidlerf  and  by  TownsendJ, 
one  of  these  is  shown  in  Fig.  5.  The  potential  gradient  required 

*  J.  J.  Thomson,  Nature,  April  23,  1896. 

t  von  Schweidler,  Wien.  Bericht,  cviii.  p.  273,  1899. 

t  J.  S.  Townsend,  Phil.  Mag.  vi.  1,  p.  198,  1901. 


12,  13] 


WHEN   IN  THE   CONDUCTING  STATE. 


13 


to   reach  this  stage  depends  upon  the  pressure  of  the  gas,  it  is 
directly  proportional  to  the  pressure ;  for  air  at  atmospheric  pressure 


60 
50 

4 

1 

30 

fo 

c 

J 

/ 

/ 

^ 

s 

x; 

90    1X0  *00     H 

V0 

Fig.  5. 

it  is  about  30,000  volts  per  centimetre,  so  that  in  air  at  a  pressure 
of  one  millimetre  a  potential  gradient  of  about  40  volts  per 
centimetre  would  be  sufficient  to  reach  this  stage. 

12.  The  saturation  current  between  two  parallel   plates  of 
given  area  depends  upon  the  amount  of  ionisation  between  the 
plates ;  if  the  ionisation  takes  place  throughout  the  whole  volume 
of  gas  between  the  plates,  then  the  greater  the  distance  between 
the  plates  the  greater  is  the  saturation  current,  so  that  if  we  use 
constant  potential  differences  large  enough  to  produce  saturation, 
the  greater  the  distance  between  the  plates  the  larger   is  the 
current.     Thus   the N  behaviour   of   the   conducting    gas   is    very 
different  from  that  of  a  metallic  or  liquid  electrolytic  conductor, 
for  if  such  conductors  were  substituted  for  the  gas  the  greater 
the  distance  between  the  plates  the  smaller  would  be  the  current. 
Under  very  small  potential  differences  however  the  three  classes 
of  conductors  would  behave  in  the  same  way. 

13.  The  peculiarities  shown  by  the  conduction  through  gases 
are  very  easily  explained  on  the  assumption  that  the  conduction  is 
due  to  ions  mixed  with  the  gas.     Let  us  for  example  take  the  case 
of  saturation.     Suppose  that  in  the  gas  between  the  plates  the 
ionising  agent  produces  in  one  second  q  positive  and  q  negative  ions 
and  let  e  be  the  magnitude  of  the  electric  charge  on  au  ion,  then 
if  an  electric  current  i  passes  between  the  plates  i/e  positive  ions 
are  driven  against  the  negative  electrode,  and  the  same  number 
of  negative  ions  are  driven  against  the  positive  electrode  in  one 


14  PROPERTIES   OF  A  GAS  [14 

second ;  thus  in  each  second  i/e  positive  and  negative  ions  are 
taken  out  of  the  gas  by  the  current.  When  the  gas  is  in  a  steady 
state  the  number  of  ions  taken  out  of  it  in  a  given  time  cannot 
be  greater  than  the  number  of  ions  produced  in  it  in  the  same 
time,  hence  i/e  cannot  be  greater  than  q,  and  thus  i  cannot  be 
greater  than  qe:  qe  is  thus  the  value  of  the  saturation  current. 
If  the  ions  are  produced  uniformly  throughout  the  gas,  and  if  qQ 
is  the  number  of  ions  produced  in  one  second  in  unit  volume,  then 
since  the  volume  of  gas  between  the  plates  is  equal  to  Al,  where 
A  is  the  area  of  one  of  the  plates  and  I  the  distance  between  the 
plates,  q  the  number  of  ions  produced  in  the  gas  in  one  second  is 
equal  to  q<)Al;  hence  the  saturation  current  is  equal  to  q<>Ale,  and 
is  thus  proportional  to  the  distance  between  the  plates.  This 
relation  between  the  saturation  current  and  the  distance  between 
the  plates  has  been  verified  by  measurements  of  the  saturation 
currents  through  gases  exposed  to  Rontgeri  rays*. 

14.  Even  when  there  is  no  current  of  electricity  passing 
through  the  gas  and  removing  some  or  all  of  the  ions,  the  number 
of  ions  present  in  the  gas  does  not  increase  indefinitely  with  the 
time  which  has  elapsed  since  the  gas  was  first  exposed  to  the 
ionising  agent ;  the  number  of  ions  in  the  gas  and  therefore  its  con- 
ductivity acquire  after  a  time  steady  values  beyond  which  they  do 
not  increase  however  long  the  ionising  agent  may  act.  This  is 
due  to  the  recombinations  that  take  place  between  the  positive 
and  negative  ions ;  these  ions  moving  about  in  the  gas  sometimes 
come  into  collision  with  each  other  and  in  a  certain  fraction  of 
such  cases  of  collision  the  positive  and  negative  ions  will  remain 
together  after  the  collision,  and  form  an  electrically  neutral  system 
the  constituents  of  which  have  ceased  to  be  free  ions.  The  collisions 
will  thus  cause  the  ions  to  disappear,  and  the  steady  state  of  a  gas 
which  is  not  carrying  an  electric  current  will  be  reached  when  the 
number  of  ions  which  disappear  in  one  second  as  the  result  of  the 
collisions  is  equal  to  the  number  produced  in  the  same  time  by 
the  ionising  agent.  Starting  from  this  principle  it  is  very  easy  to 
investigate  the  relation  between  the  number  of  free  ions  when 
the  gas  is  in  a  steady  state,  the  strength  of  the  ionising  agent, 
the  rate  at  which  the  ions  increase  on  the  first  exposure  to  the 

*  J.  J.  Thomson  and  E.  Rutherford,  Phil.  Mag.  v.  42,  p.  392,  1896. 


14]  WHEN   IN   THE   CONDUCTING   STATE.  15 

ionising  agent  and'  the  rate  at  which  they  die  away  when   the 
ionising  agent  is  cut  off. 

For  let  q  be  the  number  of  ions  (positive  or  negative)  produced 
in  one  cubic  centimetre  of  the  gas  per  second  by  the  ionising 
agent;  nlt  n^  the  number  of  free  positive  and  negative  ions 
respectively  per  cubic  centimetre  of  the  gas.  The  number  of 
collisions  per  second  between  positive  and  negative  ions  is  propor- 
tional to  rij^.  If  a  certain  fraction  of  the  collisions  result  in  the 
formation  of  a  neutral  system  the  number  of  ions  which  disappear 
per  second  in  a  cubic  centimetre  will  be  equal  to  aw^,  where  a  is 
a  quantity  which  is  independent  of  ^  and  ??2;  hence  we  have 


dn 


Thus  TC!  —  ?i2  is  constant,  so  that  if  the  gas  is  uncharged  to 
begin  with  n^  is  always  equal  to  n2.  Putting  n-^  =  n2  =  n  the 
preceding  equation  becomes 

*-«—  '  ...........................  <2>< 

the  solution  of  which  is,  if  k2  =  q/a, 


n0  the  value  of  n  when  the  gas  is  in  a  steady  state  is  obtained 
by  putting  t  equal  to  infinity  in  equation  (3)  and  is  given  by  the 
equation 

4 

n0  —  k  = 

We  see  from  equation  (3)  that  the  gas  will  not  approximate 
to  a  steady  state  until  t  is  large  compared  with  l/2&a,  that  is 
with  l/2w0a  or  1/2 V^a.  WTe  may  thus  take  1/2  V^a  as  the 
measure  of  the  time  taken  by  the  gas  to  reach  the  steady  state 
under  exposure  to  the  ionising  agent ;  as  this  time  varies  inversely 
as  V^  we  see  that  when  the  ionisation  is  feeble  it  may  take  a  very 
considerable  time  for  the  gas  to  reach  the  steady  state. 

Thus  at  some  distance,  say  a  metre,  from  an  ordinary  Rontgen 
bulb  it  may  require  an  exposure  of  a  minute  or  two  to  bring  the 
gas  into  a  steady  state. 


16  PROPERTIES  OF  A  GAS  [15 

We  may  use  equation  (2)  to  determine  the  rate  at  which  the 
number  of  ions  diminishes  when  the  ionising  agent  is  removed, 
putting  q  =  0  in  that  equation  we  have 

*--«* <4>- 

hence  n  =  - — - — - (5 ), 

1  +  n^at 

where  n0  is  the  value  of  n  when  t  =  0.  Thus  the  number  of  ions 
falls  to  one-half  its  initial  value  in  the  time  l/w0a.  We  may 
regard  equation  (4)  as  expressing  the  fact  that  a  free  ion  lasts  for 
a  time  which  on  the  average  is  equal  to  l/<m. 

15.  Equation  (4)  has  been  verified  by  Rutherford  for  gases 
exposed  to  Roritgen  rays*  and  to  the  radiation  from  uranium  f, 
by  McClungJ  for  gases  exposed  to  Rontgen  rays,  and  by 
McClelland§  for  the  case  of  gases  drawn  from  the  neighbourhood 
of  flames  and  arcs.  Two  methods  have  been  employed  for  this 
purpose.  In  one  method  air  exposed  to  rays  at  one  end  of  a  long 
tube  is  slowly  sucked  through  the  tube,  and  the  saturation  currents 
measured  at  different  parts  along  the  tube.  These  currents  are 
proportional  to  the  value  of  n  at  the  place  of  observation,  and 
knowing  the  velocity  of  the  air  and  the  distance  of  the  place  of 
observation  from  the  end  of  the  tube,  we  know  the  time  which 
has  elapsed  since  the  gas  was  ionised ;  we  can  thus  find  the  values 
of  n  corresponding  to  a  series  of  values  of  t ;  values  determined  in 
this  way  were  found  by  Rutherford  to  agree  well  with  those  given 
by  equation  (5).  This  method  can  only  be  used  when  a  large 
quantity  of  gas  is  available.  Another  method  also  used  by 
Rutherford  can  be  employed  even  for  gases  of  which  only  small 
quantities  can  be  procured.  In  this  method  gas  confined  in  a 
vessel  is  exposed  to  the  action  of  an  ionising  agent  such  as  the 
Rontgen  rays.  Inside  the  vessel  are  two  parallel  metal  plates 
A  and  B  between  which  the  ionisation  is  to  be  measured,  (in  some 
of  Rutherford's  experiments  one  of  these  plates  was  replaced  by 
the  case  of  the  vessel  which  was  made  a  conductor  by  lining  it 

*  Rutherford,  Phil.  Mag.  v.  44,  p.  422,  1897. 
t  Rutherford,  Phil.  Mag.  v.  47,  p.  109,  1899. 
t  McClung,  Phil.  Mag.  vi.  3,  p.  283,  1902. 
§  McClelland,  Phil.  Mag.  v.  46,  p.  29,  1898. 


15] 


WHEN   IN   THE   CONDUCTING   STATE. 


17 


with  wire  gauze,  the  other  plate  was  replaced  by  an  insulated 
wire  running  down  the  middle  of  the  vessel).  One  of  these 
plates  A  can  be  connected  with  an  electrometer,  the  other  jB  with 
one  terminal  of  a  large  storage  battery  the  other  terminal  of 
which  is  kept  to  earth.  A  pendulum  interrupter  is  arranged  so 
'that  as  a  heavy  pendulum  swings  it  strikes  against  levers,  and  by 
this  means  makes  or  breaks  various  connections.  While  the 
vessel  is  under  the  influence  of  the  rays,  A  and  B  are  connected 
together  and  to  earth,  then  A  is  disconnected  from  both  earth  and 
electrometer  and  left  insulated,  and  B  is  disconnected  from  the 
earth ;  the  pendulum  is  then  let  go :  as  it  falls  it  first  breaks  the 
current  going  through  the  primary  of  the  induction  coil  used  to 
excite  the  rays,  it  thus  stops  the  ionisation,  then  after  an  interval 
t  (which  can  easily  be  varied)  it  strikes  against  another  lever 
which  has  the  effect  of  connecting  B  with  the  high  potential  pole 
of  the  battery,  thus  producing  a  strong  electric  field  between  the 
plates  A  and  B:  this  field,  if  B  is  charged  positively,  drives  in  a 
very  small  fraction  of  a  second  all  the  positive  ions  which  exist 
between  A  and  B  against  A,  so  that  A  receives  a  positive  charge 
proportional  to  n ;  the  pendulum  in  its  swing  then  goes  on  to  dis- 
connect B  from  the  battery  and  connects  it  to  earth.  The  plate 
A  is  now  connected  with  the  electrometer  the  needle  of  which  is 
deflected  by  an  amount  proportional  to  the  charge  on  the  plate  A, 
i.e.  to  n.  By  adjusting  the  apparatus  so  as  to  alter  the  time 
which  elapses  between  cutting  off  the  rays  and  connecting  B  with 
the  battery  we  find  a  series  of  corresponding  values  of  n  and  t\ 
these  were  found  by  Rutherford  to  fit  in  well  with  the  relation 
indicated  by  equation  (5).  The  following  table  shows  the  rate  at 
which  the  ionisation  dies  away  in  a  special  case,  the  rate  of  course 
depends  upon  the  intensity  of  the  ionisation,  the  figures  may 
however  serve  to  give  an  idea  of  the  order  of  magnitude  of  the 
rate  of  decay  in  air  under  strong  Rontgen  radiation. 


Time  in  seconds  after 

Deflection  of 

stoppage  of  rays 

Electrometer 

•004 

184 

•08 

183 

•45 

106 

2 

37 

4 

19 

18 


PROPERTIES   OF  A   GAS 


[16 


Thus  after  4  seconds  there  was  still  a  very  appreciable  amount 
of  ionisation  -in  the  gas.  The  duration  is  still  more  marked  in  the 
following  example  when  the  radiation  was  much  weaker.  The 
electrometer  was  not  equally  sensitive  in  the  two  series  of 
experiments. 


Time 

Deflection 

•004 

174 

•45 

139 

2- 

107 

4 

54 

8 

30 

16 

16 

Thus  after  16  seconds  in  this  case  the  gas  retained  more  than 
10  per  cent,  of  its  ionisation. 

Rutherford  measured  the  rate  of  decay  in  various  gases 
exposed  to  Rontgen  rays  of  as  nearly  as  possible  the  same 
intensity.  The  results  are  shown  in  the  following  table,  the  first 
column  contains  the  name  of  the  gas,  the  second  T  the  time 
taken  for  the  ionisation  to  sink  to  one-half  of  its  original  value, 
we  have  seen  that  T=  l/ft0a=  l/V<?a;  the  third  column  contains 
relative  values  of  g,  and  the  fourth  column  the  relative  values 
of  a  calculated  from  the  values  of  T  and  q. 


Gas 

T 

q 

a 

Hydrogen 

•65 

•5 

4-8 

Air 

•3 

1 

11 

Hydrochloric  acid  gas 
Carbonic  acid  gas  
Sulphur  dioxide  
Chlorine 

•35 

•51 
•45 

18 

11 
1-2 

4 
18 

•75 
3-3 

1-25 

2 

16.  Rutherford  showed  that  the  value  of  T  was  very  much 
diminished  when  any  dust  was  present  in  the  gas,  the  dust  did 
not  however  affect  the  saturation  current.  Thus  for  example  when 
chlorine  was  first  admitted  to  the  testing  vessel  the  value  of  Twas 
•19  seconds,  after  standing  for  an  hour  T  rose  to  about  *3  seconds 


17]  WHEN   IN  THE   CONDUCTING  STATE.  19 

although  there  was  no  change  in  the  saturation  current.  Again 
for  air  which  had  been  standing  overnight  T  was  about  1  second, 
when  a  little  dusty  air  was  blown  into  the  vessel  T  fell  to  '15 
seconds,  rising  to  about  '5  seconds  in  about  10  minutes ;  it  took 
several  hours  for  T  to  rise  to  its  original  value.  Again  T  was 
found  to  be  increased  by  filtering  the  gas  through  cotton-wool. 
The  effect  produced  by  dust  is  easily  explained,  as  the  dust 
particles  are  in  all  probability  very  large  compared  with  the  ions, 
thus  if  a  positive  ion  strikes  against  a  dust  particle  and  sticks  to  it, 
it  forms  a  large  system  which  is  much  more  likely  to  be  struck  by 
a  negative  ion  and  neutralised  than  if  the  positive  ion  had  re- 
mained free ;  in  this  way  the  presence  of  dust  will  facilitate  the 
recombination  of  the  ions.  The  presence  of  dust  in  Rutherford's 
experiments  probably  explains  the  discrepancy  between  his  results 
and  Townsend's*,  who  used  dust-free  gases  and  determined  a  by 
the  first  of  the  methods  described,  care  being  taken  that  the  tubes 
through  which  the  ionised  gases  were  sucked  were  so  large  that 
the  loss  of  ions  from  diffusion  to  the  sides  of  the  tube  could  be 
neglected  in  comparison  with  those  lost  by  recombination. 
Townsend  found  that  for  air,  oxygen,  carbonic  acid,  and  hydrogen 
a  had  the  values,  34200,  33800,  35000,  and  30200,  where  0 
is  the  charge  on  the  ion  in  electrostatic  units.  We  shall  see  that 
0  is  about  3'5  x  10~10  so  that  a  for  air,  oxygen,  and  carbonic  acid  is 
about  1-2  x  lO"6  while  for  hydrogen  it  is  about  15  per  cent.  less. 
In  Rutherford's  experiments  the  value  of  a  for  air  was  about 
three  times  that  for  carbonic  acid  but  it  is  probable  that  the  gases 
in  this  case  were  not  really  dust-free. 

17.  A  series  of  careful  measurements  of  a  under  different 
conditions  would  give  us  valuable  information  as  to  the  nature  of 
the  ions;  from  some  preliminary  experiments  made  by  Dr  Nabl  at 
the  Cavendish  Laboratory  it  would  seem  that  a  is  but  little  if  at 
all  affected  by  changes  in  pressure.  Some  recent  experiments  by 
,McClungf  have  shown  that  a  is  independent  of  the  pressure,  the 
pressures  investigated  varying  from  125  to  3  atmospheres.  The 
values  found  for  a  are  for  air  and  carbonic  acid  3384  x  0  and  for 
hydrogen  2938  x  0 ;  no  experiments  seem  to  have  yet  been  made 
on  the  variation  of  a  with  temperature. 

*  Townsend,  Phil.  Trans.  A.  193,  p.  129,  1900. 
f  McClung,  Phil.  Mag.  vi.  3,  p.  283,  1902. 

2—2 


20  PROPERTIES   OF   A  GAS  [18 

Diffusion  of  Ions. 

18.  In  addition  to  the  loss  of  ions  arising  from  the  recombina- 
tion of  the  positive  and  negative  ions  there  will  be  a  further 
loss  due  to  the  diffusion  of  ions  to  the  sides  of  the  vessel. 
Thus  suppose  the  ionised  gas  is  contained  in  a  metal  vessel,  then 
when  the  ions  come  in  contact  with  the  sides  of  the  vessel  their 
charges  are  neutralised  by  the  opposite  charge  induced  on  the 
metal  and  they  thus  cease  to  act  like  ions  ;  the  layer  of  gas  next 
the  sides  of  the  vessel  is  thus  denuded  of  ions,  which  exist  in  finite 
numbers  in  the  gas  in  the  interior  ;  a  gradient  in  the  concentration 
is  thus  established  and  the  ions  diffuse  from  the  interior  to  the 
boundary.  The  problem  is  closely  analogous  to  that  of  the  absorp- 
tion of  water  vapour  in  a  vessel  whose  sides  are  wet  with  sulphuric 
acid.  We  shall  begin  by  considering  the  theory  of  a  very  simple 
case,  that  of  ionised  gas  contained  between  two  parallel  metal 
plates  at  right  angles  to  the  axis  of  x.  Let  n  be  the  number  of 
positive  ions  per  cubic  centimetre,  q  the  number  of  ions  pro- 
duced by  the  ionising  agent  per  second  in  a  cubic  centimetre 
of  the  gas,  D  the  coefficient  of  diffusion  of  the  positive  ions 
through  the  gas,  m  the  number  of  negative  ions  per  cubic  centi- 
metre, then  we  see  that  in  consequence  of  diffusion  the  rate 
of  increase  in  the  number  of  positive  ions  per  cubic  centimetre 

d?n 
is  equal  to  D  -^—  :.  assuming  that  the  surfaces  of  equal  density  of 

the  ions  are  planes  at  right  angles  to  the  axis  of  x.  Thus  taking 
recombination  and  external  ionisation  into  account  as  well  as 
diffusion  we  have 

dn  ^  d?n 


and  when  things  are  in  a  steady  state, 


Let  us  consider  the  special  case  when  the  plates  are  so  near 
together  that  the  loss  of  ions  from  diffusion  far  exceeds  that  from 
recombination,  then  we  have 


18]  WHEN   IN  THE   CONDUCTING  STATE.  21 

If  we  take  the  plane  midway  between  the  metal  plates  as 
the  plane  x  =  0,  and  if  11  is  the  distance  between  the  plates,  then 
the  conditions  to  be  satisfied  by  n  are  n  =  Q  when  x=±l;  the 
solution  of  equation  (1)  with  these  conditions  is 


.(2). 


The  total  number  of  free  positive  ions  between  the  plates  is 
equal  to 

I     ndx, 
J  -i 

and  this  by  equation  (2)  is  equal  to 


We  see  from  this  result  how  we  can  measure  D.  For,  if  we 
cut  off  the  rays  and  apply  a  strong  electric  field  between  the 
plates,  we  shall  drive  all  the  positive  ions  against  the  plate  at  the 
lower  potential,  so  that  this  plate  will  receive  a  charge  of 

electricity  equal  to  -  ^  I3e,  where  e  is  the  charge  on  an  ion  ;  if 

O     JL/ 

this  plate  is  connected  with  an  electrometer  we  can  measure  its 
charge,  which  will  be  proportional  to  the  deflection  ^  of  the 
electrometer.  If  the  rays  are  kept  on  and  the  field  is  intense 
enough  to  produce  the  saturation  current,  the  charge  received  by 
the  plate  in  one  second  is  equal  to  2qle,  hence  if  £2  is  the  deflec- 
tion of  the  electrometer  in  one  second  in  this  case,  we  see  that 


an  equation  which  enables  us  to  determine  D. 

We  have  in  this  investigation  neglected  the  effect  of  recom- 
bination; it  is  necessary  to  verify  that  the  plates  are  sufficiently 
close  together  to  make  this  justifiable.  An  easy  way  of  doing  thib 
is  as  follows  :  the  total  number  of  ions  on  the  hypothesis  that  the 
only  source  of  loss  of  ions  is  recombination  is  equal  to  21  vq/a, 
(see  p.  15);  the  number  on  the  assumption  that  the  loss  is 

entirely  due  to  diffusion  is  as  we  have  just  seen  ^  -^  I9,  hence 


if  |f>  is  small   compared  with   *l\  the  loss  of  ions  from 


o  D 


22 


PROPERTIES   OF   A   GAS 


[19 


diffusion  will  be  large  compared  with  the  loss  by  recombination, 
and  we  shall  be  justified  in  neglecting  the  latter. 

19.  The  coefficients  of  diffusion  of  the  ions  in  air,  oxygen, 
hydrogen  and  carbonic  acid  gas  have  been  determined  by  Town- 
send*  by  a  different  method;  ionised  air  being  sucked  through 
very  narrow  tubes  and  the  loss  of  ions  suffered  in  passing 
through  a  known  length  of  tubing  determined.  The  theory  of  the 
method  is  as  follows :  ionised  gas  is  sent  through  a  metal  tube  the 
axis  of  which  is  taken  as  the  axis  of  z,  the  gas  moving  parallel  to 
z  and  being  free  from  the  action  of  any  ionising  agent  in  its  course 
through  the  tube.  Consider  the  state  of  things  in  a  small  volume 
ABCDEFGH:  this  volume  loses  ions  by  diffusion,  and  gains 
them  by  the  gas  entering  the  volume  through  the  face  A  BCD 


JT 


Fig.  6. 

being  richer  in  ions  than  that  leaving  it  through  the  face 
EFGH,  when  the  gas  is  in  a  steady  state  the  rates  of  loss  and 
gain  of  ions  must  be  equal.  If  n  is  the  number  of  ions  per  cubic 
centimetre,  D  the  coefficient  of  diffusion  of  the  ions  through  the 
gas,  the  rate  of  loss  of  ions  from  diffusion  is  equal  to 

n     d?n     d?n 


If  v  is  the  velocity  of  the  gas,  the  rate  of  gain  of  ions  from  the 
second  cause  is  equal  to 

d 


or,  since  v  does  not  depend  upon  z,  to 

dn 


*  Townsend,  Phil.  Trans.  A.  193,  p.  129,  1900. 


19]  WHEN   IN  THE   CONDUCTING  STATE.  23 

Hence  equating  the  loss  and  the  gain  we  get 
n  .  d2n  .  d2n\        dn 


In  the  experiments  the  term  D~  was  very  small  compared 
with  v-^;  -^  being  of  the  order  1/20,  v  of  the  order  100  and 


D  about  "03  so  that  vn  was  about  70,000  times  D   -  .     Neglecting 

d?n 
D  ^—  and  taking  the  case  of  a  cylindrical  tube  of  radius  a  sym- 

metrical about  the  axis 

d?n     dnd*n     I  dn 


where  r  is  the  distance  of  a  point  from  the  axis  of  the  tube.    Now 

2F 

v  =  —  £-  (a2  —  r2),  where   F?ra2  is  the   volume  of  gas  passing  per 

CL 

second  through  each  cross-section  of  the  tube  ;  substituting  these 
values  in  equation  (1)  and  neglecting  d2n/dzz  we  get 


The  conditions  to  be  satisfied  by  n  are  that  n  =  0  when  r  =  a 
for  all  values  of  z,  and  that  if  the  ionised  gas  enters  the  tube  at 
z  —  0,  n  —  n0  a  constant,  when  z  =  0,  for  all  values  of  r. 


To  solve  this  equation  put  n  =  <f>e~  2F  where  <£  depends  only 
upon  r  and  6  is  a  constant  to  be  subsequently  determined  ;  substi- 
tuting this  value  of  n  in  equation  (2)  we  get 


Put  0  =  1  +  B^  +  Bft  +  Bj*  +  ..., 

and  we  get  from  (3) 


thus  the  first  three  terms  in      are 


24 


PROPERTIES   OF   A   GAS 


[19 


We  have  to  choose  such  values  of  6  that  (f>  —  0  when  r  =  a,  let 
these  values  be  Olt  02 ...  and  let  </>!,  <f>2  be  the  values  of  </>  when 
these  values  of  6  are  substituted  in  equation  (4) ;  then  we  may 
write 


To  find  the  values  of  d,  C2,  C3 ...  we  have  the  condition  n  =  n0 
a  constant  when  z  —  0.  Hence 

Now  from  the  differential  equation  (3)  we  can  easily  prove  the 
following  relations" 

I   <t>n<}>m  (&2  —  r*)rdr  =  Q  when  n  and  m  are  different  . .  .(7), 
J  o 

Multiplying  both  sides  of  equation  (6)  by  cf>n  (a2  —  r2)  r  and 
integrating  from  r  =  0  to  r  =  a  we  obtain  -by  the  aid  of  equations 
(7),  (8)  and  (9) 

Cw=~"71i 

n    dQn 
hence 

=  -KO)     i^V-.c     2F    +      ^  ^-n^e-'TF"  +  ...I .(10). 


The  number  of  ions  which  pass  across  the  section  of  the  tube 
when  s  =  0  is  7i07ra2F,  the  quantity  which  pass  across  a  section  of 
the  tube  at  a  distance  z  from  the  origin  is  equal  to 


/, 


a    2F 
«^ 


this  by  equations  (7),  (9)  and  (10)  is  equal  to 

4<7rVn0  \  1 
a      Jtfj2 


dr 


2F 


19]  WHEN   IN   THE  CONDUCTING  STATE.  25 

The  two  smallest  roots  of  the  equation  </>  =  0  were  found  by 
Townsend  to  be  01a4=7'313  and  6>2a4  =  44'56,  corresponding  to 
these  roots  we  have 


Hence  substituting  these  values  we  find  that  the  ratio  of  the 
number  of  ions  which  pass  a  cross-  section  of  the  tube  at  a  distance 
z  from  the  origin  to  the  number  which  pass  through  the  tube  at 
the  origin  is  equal  to 

7'313J>z 


4  {-1952e     **v  +  -0243e 

If  d  is  the  saturation  current  through  the  gas  after  leaving  a 
tube  of  length  llt  c2  that  after  leaving  a  tube  of  length  /2,  then 
since  the  saturation  currents  are  proportional  to  the  numbers  of 
ions  given  to  the  gas  per  second,  we  have 

d      -19526 

c 

•1952e 

Now  d/c2  can  be  determined  by  experiment,  and  hence  from 
equation  (11)  the  value  of  D  can  be  determined.  The  method 
used  by  Townsend  to  solve  this  equation  was  a  graphical  one; 

7'313_D£ 

putting  y  =  d/c2,  x  =     9  zv  1  ,  the  curve  representing  the  relation 

(11)  between  y  and  x  was  drawn  by  calculating  a  number  of  cor- 
responding values  :  when  this  curve  had  been  obtained  the  value 
of  7*313D^/2a2F  corresponding  to  any  value  of  d/Cg  obtained  by 
experiment  could  be  found,  and  hence  D  determined  as  I,  a  and  V 
are  known. 

The  apparatus  used  to  measure  the  value  of  d/Ca  is  represented 
in  Fig.  7.  A  is  a  brass  tube  50  cm.  long,  3'2  cm.  in  diameter, 
provided  with  an  aluminium  window  W  through  which  the 
Rontgeri  rays  which  ionise  the  gas  pass.  C  is  another  brass  tube 
17  cm.  long  fitting  accurately  into  A  and  able  to  slide  along  it. 
E  is  an  electrode  which  is  connected  to  a  metal  rod  F  passing 
through  an  ebonite  plug.  A  series  of  fine  wires  were  soldered 
parallel  to  one  another  and  2  mm.  apart  across  the  end  of  the 


PROPERTIES   OF   A   GAS 


[19 


tube  C.     The  gas  entered  the  apparatus  through  the  glass  tube  G 
and  then  before  reaching  the  electrode  passed  through  the  tubes  T. 


ojuu^-» 


G  vm  / 

K%%T^N 


Fig.  7. 

These  were  twelve  tubes  10  cm.  long  and  *3  cm.  in  diameter, 
arranged  at  equal  intervals  and  all  at  the  same  distance 
from  the  axis  of  the  tube  A  ;  they  were  soldered  into  holes 
bored  into  two  brass  discs  a  and  /3  which  fitted  so  closely  into  A 
that  gas  could  not  pass  between  the  disc  and  the  tube.  Another 
set  of  twelve  tubes  only  1  cm.  long  and  '3  cm.  in  diameter  were  fused 
into  another  disc  7.  The  tube  A  was  insulated  by  the  two  ebonite 
rings  R,  R'.  The  potential  of  the  tube  was  raised  to  80  volts  by 
connecting  it  with  one  of  the  terminals  of  a  battery  of  small  storage 
cells,  the  other  terminal  of  which  was  connected  with  the  earth. 
The  electrode  E  was  connected  with  one  pair  of  quadrants  of  an 
electrometer,  the  other  pair  of  quadrants  being  kept  to  earth. 
A  uniform  and  measurable  stream  of  gas  was  supplied  by  a 
gasometer,  this  gas  was  ionised  by  the  Rontgen  rays  as  it 
passed  through  the  tube,  some  of  the  ions  were  lost  by  diffusion  to 
the  sides,  all  the  positive  ones  which  escaped  were  driven  against 
the  electrode  E\  thus  the  charge  on  the  electrometer  measured 
the  number  of  positive  ions  which  got  through  the  tubes.  By 
charging  the  tube  A  up  negatively,  the  negative  ions  could  be 
driven  against  the  electrode,  and  the  number  of  those  which  get 


19] 


WHEN   IN   THE   CONDUCTING   STATE. 


27 


through  the  tubes  determined.  After  a  series  of  measurements 
had  been  made  with  the  long  tubes,  these  were  replaced  by  the 
short  ones,  and  a  similar  series  of  measurements  gone  through. 
These  measurements,  as  was  explained  in  the  preceding  theory, 
give  us  the  data  for  calculating  the  coefficient  of  diffusion  of  the 
ions.  For  gases  other  than  air,  a  somewhat  different  form  of 
apparatus  was  used,  fora  description  of  which  we  must  refer  to  the 
original  paper. 

The  loss  of  ions  even  in  the  narrow  tubes  is  not  entirely  due 
to  diffusion  to  the  sides  of  the  tube,  a  part,  though  only  a  small 
part,  of  the  loss  will  be  due  to  the  recombination  of  the  ions.  To 
estimate  how  much  was  due  to  this  effect,  the  small  tubes  Twere 
removed  and  the  deflection  of  the  electrometer  observed  when  the 
tube  C  was  placed  at  different  distances  from  the  place  where  the 
gas  is  ionised ;  in  a  wide  tube  such  as  A  the  loss  from  diffusion  to 
the  sides  is  negligible,  and  the  smaller  deflection  of  the  electro- 
meter when  the  electrode  E  is  moved  away  from  the  place  of 
ionisation  is  due  to  the  loss  of  ions  by  recombination.  By  making 
measurements  at  different  distances  and  knowing  the  velocity  of 
the  gas  we  can  measure  in  this  way  the  amount  of  recombination 
taking  place  in  a  given  time  and  hence  determine  the  value  of  a, 
the  constant  of  recombination.  It  was  in  this  way  that  the  values 
of  a  given  on  page  19  were  determined.  Knowing  a  it  is  easy  to 
calculate  the  loss  of  ions  from  recombination  in  their  passage 
through  the  narrow  tubes,  and  then  to  apply  a  correction  to  the 
observations  so  as  to  get  the  loss  due  to  diffusion  alone. 

The  following  tables  give  the  velocities  of  the  coefficients  of 
diffusion  on  the  C.G.s.  system  of  units  as  deduced  by  Townsend 
from  his  observations. 

TABLE  I.    COEFFICIENTS  OF  DIFFUSION  IN  DRY  GASES. 


Gas 

D  for  +  ions 

D  for  -  ions 

Mean  value 
ofD 

Ratio  of  D  for 
-  to  D  for 
+  ions 

Air  

•028 

•043 

•0347 

1-54 

Oxygen    

•025 

•0396 

•0323 

1-58 

Carbonic  acid  
Hydrogen       .  . 

•023 
•123 

•026 
•190 

•0245 
•156 

1-13 
1-54 

28 


PROPERTIES   OF   A   GAS 


[19 


TABLE  II.    COEFFICIENTS  OF  DIFFUSION  IN  MOIST  GASES. 


Gas 

D  for  +  ions 

D  for  -  ions 

Mean  value 
of  D 

Eatio  of  D  for 
-  to  +  ions 

Air          

•032 

•035 

•0335 

1-09 

Oxygen    

•0288 

•0358 

•0323 

1-24 

Carbonic  acid 

•0245 

•0255 

•025 

1-04 

Hydrogen    . 

•128 

•142 

•135 

I'll 

We  see  from  these  tables  that  the  coefficient  of  diffusion  for 
the  negative  ions  is  greater  than  that  for  the  positive,  the  difference 
being  much  more  marked  in  dry  than  in  damp  gases.  The  superior 
mobility  of  the  negative  ions  was  first  observed  by  Zeleny*  who 
measured  by  a  method  which  we  shall  shortly  describe  the  velocity 
of  the  ions  when  placed  in  an  electric  field,  and  found  that  the 
negative  ions  moved  faster  than  the  positive  ones.  The  more 
rapid  diffusion  of  the  negative  ions  explains  why  in  certain  cases 
ionised  gas,  originally  electrically  neutral,  acquires  a  charge  of 
positive  electricity.  Thus,  for  example,  if  such  a  gas  is  blown 
through  metal  tubes,  the  gas  emerging  from  the  tubes  will  be 
positively  electrified,  as  in  the  passage  through  the  tubes  it  has 
lost  more  negative  than  positive  ions.  Zeleny  (loc.  cit.)  has  shown 
that  this  effect  does  not  occur  with  carbonic  acid  gas  in  which  the 
velocities  of  the  two  ions  are  very  nearly  equal.  Some  experi- 
ments made  by  Rutherfordf  seem  to  show  that  in  addition  to  the 
effect  produced  by  diffusion,  there  is  a  specific  effect  due  to  the 
metal,  as  he  found  that  the  excess  of  positive  over  negative  ions 
was  greater  when  the  ionised  gas  passed  through  zinc  tubes  than 
when  it  passed  through  copper.  The  difference  in  the  rate  of 
diffusion  of  the  positive  and  negative  ions  causes  a  certain  amount 
of  electrical  separation  to  take  place  when  a  gas  is  ionised  ;  as  the 
negative  ions  diffuse  more  rapidly  than  the  positive  ones,  the 
region  where  ionisation  takes  place  will  have  an  excess  of  positive 
ions  and  be  positively  electrified,  while  in  consequence  of  the 
diffusion  of  the  negative  ions  the  surrounding  regions  will  have  an 
excess  of  these  ions  and  will  therefore  be  negatively  electrified. 

*  Zeleny,  Phil.  Mag.  v.  46,  p.  120,  1898. 

t  Kutherford,  Phil.  Mag.  v.  43,  p.  241,  1897. 


19] 


WHEN   IN   THE   CONDUCTING   STATE. 


29 


The  results  given  in  Tables  I.  and  II.  show  that  the  excess  of 
the  velocity  of  diffusion  of  the  negative  ions  over  that  of  the 
positive  is  much  greater  when  the  gas  is  dry  than  when  it  is 
moist ;  the  effect  of  moisture  on  the  velocity  of  diffusion  is  very 
remarkable,  the  results  quoted  in  the  table  show  that  with  the 
exception  of  ions  in  carbonic  acid  (where  there  is  but  little  differ- 
ence between  the  velocities  of  diffusion  of  positive  or  negative  ions 
in  either  wet  or  dry  gas)  the  effect  of  moisture  is  to  produce  a 
very  considerable  diminution  in  the  rate  of  diffusion  of  the  negative 
ions,  while  on  the  other  hand  it  tends  to  increase  the  rate  of  dif- 
fusion of  the  positive  ions,  though  the  change  produced  in  the 
positive  ions  is  not  in  general  as  great  as  that  produced  in  the 
negative.  We  shall  see  later  on  that  water  vapour  condenses 
more  readily  on  negative  ions  than  on  positive  ones,  so  that  it  is 
probable  that  the  negative  ions  in  a  damp  atmosphere  get  loaded 
with  moisture  and  so  are  retarded  in  their  movements  through  the 
surrounding  gas. 

The  preceding  experiments  relate  to  ions  produced  by  the 
Rontgen  rays.  Townsend*  subsequently  applied  the  same  method 
to  the  determination  of  the  coefficients  of  diffusion  of  ions  pro- 
duced by  radio-active  substances,  by  ultra-violet  light  and  by 
discharges  from  electrified  needle  points ;  the  results  of  these 
experiments  are  shown  in  the  following  table. 

COEFFICIENTS  OF  DIFFUSION  OF  IONS  PRODUCED  IN  AIR  BY 
DIFFERENT  METHODS. 


Method 

Dry  Air 

Moist  Air 

+  ions 

-  ions 

+  ions 

-  ions 

Rontgen  rays    

•028 
•032 

•0247 
•0216 

•043 
•043 
•043 
•037 
•032 

•032 
•036 

•028 
•027 

•035 
•041 
•037 
•039 
•037 

Radio-active  substances  ... 
Ultra-violet  light         

Point  Discharge  

From  these  numbers  we  conclude  that  the  ions  produced  by 
Rontgen  rays,  by  radio-active  substances  and  by  ultra-violet  light 

*  Townsend,  Phil.  Trans.  A.  195,  p.  259,  1900. 


30 


PROPERTIES   OF   A   GAS 


[20 


are  identical,  a  conclusion  which  we  shall  find  confirmed  by  several 
other  courses  of  reasoning. 

Townsend*  also  investigated  the  coefficients  of  diffusion  of  ions 
produced  by  radio-active  substances  at  a  series  of  pressures  ranging 
from  772  millimetres  of  mercury  to  200  mm.  and  found  that  within 
this  range  the  coefficient  of  diffusion  was  inversely  proportional  to 
the  pressure ;  the  Kinetic  Theory  of  Gases  shows  that  this  would 
be  true  in  a  system  where  the  diffusing  systems  do  not  change 
character  with  the  pressure ;  as  this  result  holds  for  ions  we  con- 
clude that  down  to  a  pressure  of  at  least  200  mm.  the  ions  do  not 
change.  We  shall  see  that  at  very  low  pressures  the  negative  ions 
are  very  much  smaller  than  at  these  high  pressures. 

20.  It  is  of  interest  to  compare  the  rates  of  diffusion  of  ions 
through  a  gas  with  those  of  the  molecules  of  one  gas  through 
another.  In  the  following  table  taken  from  Winkelmann's  Hand- 
buck  der  Physik,  vol.  i.  pp.  645,  647,  the  coefficients  of  diffusion 
into  each  other  for  hydrogen,  air,  carbonic  acid,  and  carbonic  oxide, 
and  for  some  vapours  are  given;  it  appears  from  the  table  that 
the  gases  diffuse  very  much  more  quickly  than  the  ions,  but  that 
there  are  vapours  whose  coefficients  of  diffusion  are  of  the  same 
order  as  those  of  the  ions. 


Gas 

D 

cm.2/sec. 

Gas 

D 

cm.2/sec. 

Gas 

D 

cm.2/sec. 

CO—  C02 

•13142 

CO—  02 

•18717 

ether—  CO2 

•0552 

air—  C02 
02-C02 

•13433 
•13569 

H2-02 
H2  —  air 

•66550 
•63405 

isobutylic  )      TT 
amide      )         2 

•1724 

H2—  C02 

•53409 

i  ether—  H2 

•296 

„        —air 

•0426 

air  —  O2 

•17778 

ether  —  air 

•0775 

•0305 

| 

The  most  probable  explanation  of  the  slow  diffusion  of  the 
ions  seems  to  be  that  the  charged  ion  forms  a  nucleus  round 
which  the  molecules  of  the  gas  condense,  just  as  dust  collects  round 
a  charged  body,  thus  producing  a  complex  system  which  diffuses 
slowly :  this  explanation  is  supported  by  the  fact  discovered  by 
McClelland'fp  that  the  coefficients  of  diffusion  of  the  ions  in  the 
flame  gases  depend  very  much  on  the  temperature  of  the  flame 

*  Townsend,  Phil.  Trans.  A.  195,  p.  259,  1900. 

f  McClelland,  Camb.  Phil.  Soc.  Proc.  x.  p.  241,  1899. 


21]  WHEN  IN  THE   CONDUCTING  STATE.  31 

and  the  distance  of  the  ions  from  it ;  a  comparatively  small 
lowering  of  temperature  producing  a  great  diminution  in  the  rate 
of  diffusion  of  the  ions,  as  if  precipitation  had  occurred  upon 
them.  The  view  is  also  supported  by  the  ability  of  the  ions  to 
act  as  nuclei  for  the  precipitation  of  water  vapour.  It  must  be 
remembered  also  that  an  ion  differs  from  an  ordinary  molecule  in 
being  charged  with  electricity  and  thus  being  surrounded  by  a 
strong  electric  field. 

Rutherford*  has  recently  shown  that  the  vapour  of  alcohol  or 
ether,  like  that  of  water,  produces  a  great  diminution  in  the 
mobility  of  the  negative  ion. 

Velocity  of  the  Ions  in  an  Electric  Field. 

21.  The  coefficient  of  diffusion  of  the  ions  through  a  gas  is 
directly  proportional  to  the  speed  with  which  the  ions  travel 
through  the  gas  under  the  action  of  an  electric  field  of  given 
strength.  The  connection  between  this  speed  and  the  coefficient 
of  diffusion  can  be  established  as  follows.  From  the  definition  of 
the  coefficient  of  diffusion  D  it  follows  that  if  n  is  the  number  of 
ions  per  cubic  centimetre,  the  number  of  ions  which  in  unit 
time  cross  unit  area  of  a  plane  at  right  angles  to  x  is  equal  to 

D  -j-  .     We  may  thus  regard  the  ions  as  moving  parallel  to  the 

axis  of  x  with  the  average  velocity  —D-j—.     The  ions  being  in 

the  gaseous  state  will  produce  a  partial  pressure  p  which  when 
the  temperature  is  constant  is  proportional  to  the  number  of  ions, 
we  see  therefore  that  the  average  velocity  of  the  ions  parallel 

to  x  is  equal  to  -D-f.     Now  dp  Idas  is  the  force  acting  parallel 
p      dx 

to  the  axis  of  x  on  unit  volume  of  the  gas,  we  may  thus  interpret 
the  preceding  expression  as  meaning  that  when  the  force  acting 
parallel  to  the  axis  of  x  on  the  ions  in  unit  volume  is  unity,  the 
ions  move  parallel  to  the  axis  of  x  with  a  mean  velocity  of  transla- 
tion equal  to  Djp.  Suppose  now  that  the  ions  are  placed  in  an 
electric  field  when  the  electric  intensity  parallel  to  the  axis  of  x 
is  equal  to  X,  then  the  force  on  the  ions  in  unit  volume  is  equal 

*  Eutherford,  Phil.  Mag.  vi.  2.  p.  210,  1901. 


32  PROPERTIES  OF  A  GAS  [22 

to  Xen,  hence  if  u  is  the  average  velocity  of  translation  of  the 
ions  parallel  to  the  axis  of  x 

u  =  Xen  —  . 
P 

Now  n/p  is  the  same  for  all  gases  at  the  same  temperature, 
hence  if  N  is  the  number  of  molecules  of  air  in  a  c.c.  at  this 
temperature  and  at  the  atmospheric  pressure  II,  since  n/p  —  N/Tl, 
we  have 


or  u0  the  velocity  of  the  ions  in  a  field  of  unit  intensity  is  given 
by  the  equation 

r\Ne 

m-D^-. 

Thus  u0  is  directly  proportional  to  D,  so  that  a  knowledge  of 
one  of  these  quantities  enables  us  at  once  to  calculate  the  other. 

22.  Measurements  of  the  velocity  of  the  ions  under  an 
electric  field  were  made  some  time  before  those  of  the  coefficients 
of  diffusion.  The  earliest  systematic  measurements  of  the  velocity 
of  the  ions  in  an  electric  field  were  made  in  the  Cavendish 
Laboratory  in  1897  by  Rutherford*.  Two  different  methods  were 
used  in  these  experiments.  The  first  method  is  as  follows  : 
suppose  that  the  current  is  passing  through  ionised  gas  between 
two  parallel  plates  A  and  B  ;  then  if  there  are  n  positive  ions  and 
n  negative  ions  in  each  cubic  centimetre  of  the  gas  and  ulf  u2  are 
respectively  the  velocities  of  the  positive  and  negative  ions,  the 
current  i  passing  through  each  unit  area  of  cross-section  between 
the  plates  is  given  by  the  equation 

i  =  n  (H!  +  u2)  e, 

where  e  is  the  charge  on  an  ion.  Now  i  can  easily  be  measured  if 
one  of  the  plates  A  is  connected  to  one  pair  of  quadrants  of  an 
electrometer,  the  other  pair  of  which  is  connected  to  earth,  and 
if  the  other  plate  B  is  connected  to  one  terminal  of  a  battery  of 
known  electromotive  force,  the  other  terminal  of  which  is  to 
earth.  For  if  the  quadrants  are  at  first  connected  together  and 
then  disconnected,  i  will  be  the  charge  communicated  in  one 
second  to  the  plate  connected  with  the  electrometer. 

*  Rutherford,  Phil.  Mag.  v.  44,  p.  422,  1897. 


22]  WHEN   IN  THE   CONDUCTING  STATE.  33 

The  value  of  ne  can  be  determined  in  the  following  way; 
after  the  gas  has  been  exposed  to  the  ionising  agent,  say 
Rontgen  rays,  sufficiently  long  for  it  to  get  into  a  steady 
state,  the  rays  are  suddenly  cut  off,  and  simultaneously  with 
the  extinction  of  the  rays  a  large  electromotive  force  is  suddenly 
switched  on  between  the  plates;  then  if  B  is  the  positive  plate  all 
the  positive  ions  between  the  plates  are  driven  against  the  plate 
A  before  they  have  time  to  recombine  with  the  negative  ions,  and 
thus  A  receives  a  positive  charge  equal  to  that  on  the  whole  of 
the  positive  ions  between  the  plates,  i.e.  each  unit  area  of  A 
receives  a  charge  of  positive  electricity  equal  to  nle,  where  /  is  the 
distance  between  the  plates.  This  charge  can  be  measured  by  the 
electrometer,  let  it  equal  q ;  then  since  i  =  n  (u^  +  u2)  e,  we  have 

i  _  M!  +  u2 

q~       I  1}' 

a  relation  which  enables  us  to  determine  u^  +  Uz.  Now  let  E  be 
the  potential  difference  between  the  plates  when  the  current  is  i. 
Then  u^  +  u2  is  the  sum  of  the  velocities  of  the  ions  when  the 
electric  intensity  is  Ejl ;  hence,  since  as  we  shall  see  the  velocity 
of  an  ion  is  proportional  to  the  electric  intensity,  the  sum  of  the 
velocities  of  the  positive  and  negative  ions  when  the  electric 
intensity  is  unity  is  (u^  +  u2)  l/E,  or  I2i/Eq.  For  this  method  to 
give  accurate  results,  the  ionisation  and  the  electric  field  must  be 
uniform  between  the  plates  ;  this  condition  requires,  as  the  investi- 
gation in  Chapter  III.  shows,  that  the  current  should  be  so  small 
that  the  conduction  is  in  the  stage  represented  by  the  first 
part  of  the  curve,  Fig.  4,  when  the  curve  is  straight  and  the 
current  is  proportional  to  the  electric  intensity.  Again,  when  the 
ionisation  is  produced  by  Rontgen  rays  or  the  rays  from  a  radio- 
active substance,  the  rays  should  be  arranged  so  that  they  pass 
tangentially  between  the  plates  and  do  not  strike  against  them ; 
the  reason  for  this  precaution  is  that  when  the  rays  strike  against 
a  metallic  surface,  there  is  an  abnormally  great  ionisation  of  the 
gas  close  to  the  surface  of  the  plates  and  the  ionisation  between 
the  plates  is  not  uniform. 

The  values  for  the  sum  of  the  velocities  of  the  positive  and 
negative  ions  under  a  potential  gradient  of  one  volt  per  centimetre 
obtained  by  Rutherford  by  this  method  are  given  in  the  following 
table. 
T.  G. 


34 


PROPERTIES   OF   A   GAS 


[23 


Gas 

Sum  of  velocities 
of  +  and  -  ions 

Gas 

Sum  of  velocities 
of  +  and  -  ions 

Hydrogen 

10     cm.  /sec. 

Carbonic  acid 

2*15  crn./sec. 

2  *8  cm.  /sec. 

Sulphur  dioxide  ... 

*99  cm.  /sec. 

Nitrogen  

3  '2  cm.  /sec. 

Chlorine  

2       cm.  /sec. 

Air 

3  '2  cm.  /sec. 

Hydrochloric  acid 

2*55  cm./sec. 

In  these  experiments  the  gases  were  not  specially  dried. 

23.  The  method  in  this  form  can  only  be  used  when  there  is 
a  considerable  volume  of  gas  between  the  plates  and  when  the 
ionisation  is  large,  in  other  cases  the  deflection  of  the  electrometer 
obtained  when  the  large  electromotive  force  is  applied  between  the 
plates  is  so  small  that  accurate  determinations  of  q  are  not  possible; 
thus  if  the  distance  between  the  plates  is  3'2  cm.  we  see  from 
equation  (1)  that  the  deflection  of  the  electrometer,  when  the 
large  electromotive  force  is  applied,  is  only  that  produced  in  one 
second  by  the  steady  leak  caused  by  a  potential  difference  of  8*2 
volts  between  the  plates ;  this  with  a  fairly  sensitive  electrometer 
and  not  very  weak  ionisation,  would  often  not  exceed  2  or  3  scale 
divisions,  while  the  percentage  error  with  such  small  deflections 
would  be  very  large.  I  have  used  a  modification  of  this  method 


Earth 


Earth 


Electrometer 


Earth 


Fig.  8. 

which  is  not  subject  to  these  disadvantages.     The  arrangement 
is  represented  diagrammatically  in  Fig.  8.     C  is  the  plate  con- 


23]  WHEN   IN   THE   CONDUCTING   STATE. 


35 


nected  with  the  electrometer,  it  is  provided  with  a  guard  ring  so 
as  to  avoid  difficulties  connected  with  irregularities  in  the  electric 
field:  this  plate  is  placed  between  two  parallel  plates  A  and  B 
and  the  whole  region  between  A  and  B  is  exposed  to  the  ionising 
agent.  The  plates  are  adjusted  so  that  the  rate  of  leak  to  the 
plate  G,  when  A  is  charged  to  a  potential  V  and  B  connected 
with  earth,  is  the  same  as  that  to  G,  when  B  is  charged  to  the 
potential  V  and  A  is  connected  with  earth. 

A  is  connected  to  a  point  E  in  a  high  resistance  GH  which  is 
traversed  by  the  current  from  the  voltaic  cell  F,  H  is  connected 
with  earth,  and  by  moving  the  point  of  attachment  E  the  plate  A 
can  be  raised  to  any  potential  from  zero  up  to  the  electromotive 
force  of  the   battery ;   if   G  is  the  positive  pole  of  the  battery 
positive  electricity  will  flow  into  the  plate  C  (this  plate  is  initially 
connected  with  earth).     B  is  connected  with  the  earth  through  a 
large  resistance  ft,  the  point  8  is  touched  at  regular  intervals  by 
a  rotating  brush  which  connects  it  for  a  very  short  time  with  the 
negative  terminal  of  a  large  battery  of  small  storage  cells  the 
other  terminal    of   which    is  to   earth.     The   contact   lasts   long 
enough  for  the  electric  field  to  drive  all  the  negative  ions  between 
B  and  C  on  to  the  plate  C,  but  not  long  enough  for  any  appre- 
ciable quantity  of  fresh  ions  to  be  produced  while  the  field  is  on. 
The   plate   C  is  thus  receiving  positive  ions   from  one  side  and 
negative  from  the  other,  and  by  moving  the  point  E  about  we  can 
make  the  positive  charge  balance  the  negative  so  that  there  is  no 
deflection  of  the  electrometer.     When   this  is  the  case  we  can 
easily  prove  by  the  same  reasoning  as  before  that  KI  4-  vlt  the  sum 
of  the  velocities   of  the    positive  and    negative   ions  when  the 
potential  difference  between  the  plates  A  and  C  is  equal  to  that 
between  E  and  H,  is  equal  to  ml  where  I  is  the  distance  between 
the  plates  B  and  (7,  and  m  is  the  number  of  contacts  per  second 
made  by  the  rotating  brush  with  S.     As  in  this  case  the  experi- 
ment may  be  made  to  last  while  a  large  number  of  contacts  occur, 
the  method  is  much  more  sensitive  than  when  only  one  contact  is 
made. 

To  prevent  the  potential  of  G  changing  appreciably  in  the 
interval  between  the  contacts,  C  is  connected  with  one  of  the 
plates  of  a  parallel  plate  condenser  of  large  capacity.  When  the 
final  test  is  made  as  to  whether  C  has  or  has  not  received  a  charge 

3—2 


PROPERTIES   OF   A   GAS 


[24 


the  plates  of  the  condenser  are  pulled  apart  so  as  to  diminish  its 
capacity  and  thus  increase  the  deflection  of  the  electrometer  due 
to  any  charge  that  might  be  on  the  plate  C.  Care  must  be  taken 
to  allow  sufficient  time  to  elapse  between  successive  contacts  at  S 
to  permit  of  the  gas  getting  into  a  steady  state  before  the  next 
contact  is  made.  When  the  ionisation  is  very  weak  it  may 
require  an  interval  of  several  seconds  for  this  condition  to  be 
fulfilled. 

24.     Another  method  used  by  Rutherford*  is  represented  in 
Fig.  9.     Two  large  metal  plates  A  and  B  were  placed  parallel  to 


" 

Earth 


Lever 

M 


.// 


r  To  Battery 
A         of  cells 


F!// 

-©- 


j 


Fig.  9. 


one  another  and  16  cms.  apart  on  the  insulating  blocks  C  and  D. 
The  Rontgen  rays  were  arranged  so  as  to  pass  through  only  one 
half  of  the  gas  included  between  the  plates,  thus  no  direct  radia- 
tion reached  the  air  to  the  left  of  the  line  EF  which  is  half-way 
between  the  plates.  The  plate  A  was  connected  with  one  terminal  of 
a  battery  of  a  large  number  of  small  storage  cells  giving  a  potential 
difference  of  220  volts,  the  other  terminal  of  the  battery  being  con- 
nected with  the  earth.  The  plate  B  was  connected  through  a  contact 
lever  LM,  mounted  on  an  insulating  block,  to  one  pair  of  quadrants 
of  an  electrometer,  the  other  pair  being  connected  with  the  earth, 


*  Rutherford,  Phil.  Mag.  v.  44,  p.  422,  1897. 


25]  WHEN   IN   THE   CONDUCTING  STATE.  37 

A  pendulum  interrupter  was  arranged  so  as  first  to  make  the  current 
in  the  primary  of  the  induction  coil  used  to  produce  the  rays, 
then  after  a  known  interval  to  break  the  electrometer  circuit  by 
knocking  away  the  lever  LM,  and  then  to  break  the  battery  circuit 
shortly  afterwards.  N  is  a  condenser  connected  to  the  electrometer 
to  increase  its  capacity.  With  this  arrangement  the  ions  have  to 
travel  over  a  distance  of  8  cm.  before  they  reach  the  plate  B,  and 
the  object  of  the  experiment  was  to  find  the  time  occupied  by  the 
rays  in  passing  over  this  distance.  It  was  found  that  there  was 
only  a  very  small  deflection  of  the  electrometer  when  the  interval 
between  putting  on  the  rays  and  breaking  the  electrometer  circuit 
was  less  than  '36  sec.,  but  when  the  interval  exceeded  this  value 
the  deflection  of  the  electrometer  increased  rapidly.  Thus  '36  sec. 
was  taken  as  the  time  required  for  the  ions  to  pass  over  a  distance 
of  8  cm.  under  a  potential  gradient  of  220/16  volts  per  centimetre. 
This  corresponds  to  a  velocity  T6  cm./sec.  for  the  gradient  of  a 
volt  per  centimetre,  and  no  difference  was  detected  between  the 
velocities  of  the  positive  and  negative  ions.  This  makes  the  sum 
of  the  velocities  of  the  positive  and  negative  ions  in  air  under  a 
potential  gradient  of  a  volt  a  centimetre  equal  to  3'2  cm./sec. 
which  is  exactly  the  velocity  found  by  Rutherford  using  the  first 
method. 

25.  The  difference  between  the  velocities  of  the  positive  and 
negative  ions  was  discovered  by  Zeleny*,  who  has  made  very 
valuable  determinations  of  the  velocities  of  the  ions  in  an  electric 
field.  The  method  by  which  he  discovered  the  difference  of  the 
velocities  was  by  finding  the  electric  force  required  to  force  an  ion 
against  a  stream  of  gas  moving  with  a  known  velocity  parallel 
to  the  lines  of  electric  force.  Thus  suppose  A  and  B,  Fig.  10, 
represent  two  parallel  plates  made  of  wire  gauze  and  that  between 
these  plates  we  have  a  stratum  of  ionised  gas,  let  the  gas  be 
moving  through  the  plates  from  A  to  B  with  the  velocity  V,  and  let 
the  potential  gradient  between  the  plates  be  n  volts  per  centimetre, 
B  being  the  positive  plate.  Then  if  the  velocity  of  the  positive  ion 
under  a  potential  gradient  of  1  volt  per  centimetre  be  u,  the  velo- 
city of  the  positive  ion  in  the  direction  from  B  to  A  is  nu  —  V  and 
this  is  proportional  to  the  number  of  ions  giving  up  their  charges 

*  Zeleny,  Phil.  Mag.  v.  46,  p.  120,  1898. 


38 


PROPERTIES   OF  A  GAS 


[25 


to  A  in  unit  time.     Suppose  now  that  we  make  B  the  negative 
plate,  then  if  the  potential  gradient  between  the  plates  is  ri  volts 


d 

u 


B 


Fig.  10. 

per  centimetre  and  the  velocity  of  the  negative  ion  under  a 
potential  gradient  of  1  volt  per  centimetre  is  v,  the  velocity  of 
the  negative  ion  from  B  to  A  is  n'v  —  V,  and  this  is  proportional 
to  the  number  of  negative  ions  giving  up  their  charges  to  A 
in  unit  time.  If  we  adjust  the  potential  gradients  so  that  the 
rate  at  which  A  receives  a  positive  charge  when  B  is  positive  is 
equal  to  the  rate  at  which  it  receives  a  negative  charge  when  B  is 
negative,  we  have 

nu  —  V—n'v  —  V, 


or 


Thus  from  the  measurement  of  the  potential  gradients  we  can 
determine  the  ratio  u  :  v. 

The  apparatus  used  by  Zeleny  for  carrying  out  this  method  is 
shown  in  Fig.  11.  P  and  Q  are  brass  plates  9  centimetres  square. 
They  are  bored  through  their  centres  and  to  the  openings  thus 
made  the  tubes  R  and  $  are  attached,  the  space  between  the 
plates  being  covered  in  so  as  to  form  a  closed  box ;  K  is  a  piece  of 
wire  gauze  completely  filling  the  opening  in  the  plate  Q ;  T  is  an 


25] 


WHEN   IN   THE   CONDUCTING  STATE. 


39 


insulated  piece  of  wire  gauze  nearly  but  not  quite  filling  the  open- 
ing in  the  plate  P  and  connected  with  one  pair  of  quadrants  of  an 


Earfh 


Fig.   11. 

electrometer  E.  A.  plug  of  glass-wool  G  filters  out  the  dust  from 
a  stream  of  gas  which  enters  the  vessel  by  the  tube  D  and  leaves 
it  by  .P;  this  plug  has  also  the  effect  of  making  the  velocity  of 
flow  of  the  gas  uniform  across  the  section  of  the  tube.  The 
Rontgen  rays  to  ionise  the  gas  were  produced  by  a  bulb  at  0,  the 
bulb  and  coil  being, in  a  lead-covered  box  fitted  with  an  aluminium 
window  through  which  the  rays  passed.  Q  is  connected  with  one 
pole  of  a  battery  of  cells  and  P  and  the  other  pole  of  the  battery 
connected  with  earth.  When  the  rays  are  entering  PQ  and  the 
ions  are  travelling  in  opposite  directions  in  the  box  the  charges 
they  give  to  P,  Q  and  K  are  conducted  to  earth,  while  those  they 
give  to  T  gradually  change  its  potential  at  an  approximately 
uniform  rate,  as  long  as  this  potential  is  small  compared  with  that 
of  Q.  When  the  distribution  of  free  charges  in  the  gas  has 
assumed  a  steady  state  all  the  changes  in  the  potential  of  T  are 
due  to  the  charges  given  up  by  the  ions  striking  against  it. 

The  nature  of  the  readings  obtained  with  this  apparatus  are 
indicated  by  the  curves  shown  in  Fig.  12  where  the  ordinates 
represent  the  deflection  of  the  electrometer  in  a  given  time  and 
the  abscissse  the  potential  difference  in  volts  between  the  plates 
P  and  Q.  Curve  I.  is  for  the  case  when  the  negative  ions,  Curve 
II.  when  the  positive  ions,  are  driven  against  the  plate.  It  will 
be  seen  that  after  a  point  about  B  the  curves  are  for  some  distance 


40 


PROPERTIES   OF   A   GAS 


[25 


straight  lines,  but  that  there  is  a  curved  portion  to  the  left  of  B,  in- 
dicating that  some  ions  are  delivered  up  to  the  gauze  under  smaller 


20         30          40          50          60         70          80         90 


voltages  than  we  should  expect.  This  may  possibly  be  explained 
by  irregularities  in  the  air  blast,  the  deflections  corresponding  to 
the  part  of  the  curve  about  A  arriving  in  the  lulls  of  the  blast.  One 
way  of  treating  the  observations  would  be  to  produce  the  straight 
portion  of  the  curves  until  they  cut  the  horizontal  axis ;  in  the 
figure  this  would  happen  for  Curve  I.  at  about  50  volts  and  for 
Curve  II.  at  about  60 ;  we  might  then  take  50  volts  as  the 
potential  difference  between  the  plates  which  would  give  to  the 
negative  ions  a  velocity  equal  to  that  of  the  blast,  while  60  volts 
would  be  required  to  give  the  same  velocity  to  the  positive  ions, 
so  that  under  fields  of  equal  strength  the  velocity  of  the  negative 
ion  would  be  to  that  of  the  positive  as  6  to  5.  The  method  actually 
adopted  was  different ;  the  curves  were  regarded  as  merely  a 
preliminary  part  of  the  experiment  indicating  about  the  values  of 
the  potential  differences  to  employ  in  the  final  observations.  Thus 
from  the  curves  in  Fig.  12  it  is  clear  that  to  get  the  same  deflec- 
tion with  the  positive  ions,  as  is  got  with  the  negative  ions  for  a 
potential  difference  of  60  volts,  would  require  a  potential  difference 
of  between  72  and  74  volts;  a  careful  series  of  measurements  with 
differences  of  potential  between  these  values  .is  taken  and  the  true 


26] 


WHEN   IN   THE   CONDUCTING   STATE. 


41 


value  of  the  potential  difference  found  by  interpolation.  When 
this  value,  suppose  for  example  73'2,  had  been  found,  the  ratio 
of  the  velocities  of  the  negative  to  the  positive  ions  was  taken 
as  73-2  :  60. 

The  potential  gradient  between  the  plates  was  found  to  be  not 
quite  uniform  owing  to  the  accumulation  of  ions  between  the 
plates.  The  actual  potential  gradient  was  measured  and  a  correc- 
tion applied  for  the  want  of  uniformity,  this  correction  amounted  to 
about  2  per  cent.  The  results  obtained  by  Zeleny  are  given  in 
the  following  table. 

RATIO  OF  VELOCITIES  OF  IONS. 


Gas 

Velocity  of  negative  ion 

Velocity  of  positive  ion 

Air 

1'24 

Oxygen  

1-24 

Nitrogen    

1-23 

Hydrogen  ;  

1-14 

Coal  gas 

1-15 

Carbon  dioxide  

1-00 

Ammonia  

1-045 

Acetylene 

0-985 

Nitrogen  monoxide  .  .  . 

1-105 

Thus  acetylene  is  the  only  gas  in  which  the  velocity  of  the 
negative  ion  is  less  than  that  of  the  positive  and  here  the  differ- 
ence is  so  small  that  it  is  within  the  limits  of  error  of  the  experi- 
ment. The  gases  in  this  experiment  were  not  specially  dried; 
we  have  seen  that  moisture  has  a  great  effect  in  reducing  the 
velocity  of  the  negative  ion. 

26.  In  some  later  experiments  Zeleny*  has  determined  the 
absolute  values  of  the  velocity  of  both  the  positive  and  negative 
ions.  The  method  he  employed  was  a  blast  method,  though  in 
these  experiments  the  blast  was  at  right  angles  to  the  lines  of 
electric  force  instead  of  along  them.  A  method  similar  to  the 
one  just  described  was  tried  for  a  considerable  time  (it  is  evident 
that  if  we  know  the  velocity  of  the  blast  and  the  points  where 

*  Zeleny,  Phil.  Trans.  A.  195,  p.  193,  1900. 


42 


PROPERTIES   OF   A   GAS 


[26 


the  straight  portions  of  the  Curves  I.  and  II.  cut  the  horizontal 
axis  we  can  deduce  the  velocity  of  both  the  positive  and  negative 
ions),  but  it  had  to  be  abandoned  owing  to  the  disturbance  in  the 
distribution  of  the  velocity  of  the  blast  caused  by  the  wire  gauze 
which  in  this  method  has  to  be  used  for  the  electrodes. 

The  theory  of  the  method  finally  used  is  as  follows.  A  stream 
of  gas  flows  between  two  concentric  metal  cylinders  which  are 
kept  at  different  potentials,  the  gas  at  one  place  is  traversed  by 
a  beam  of  Rontgen  rays  at  right  angles  to  the  axis  of  the  cylinder ; 
the  ions  thus  produced  are  carried  by  the  stream  of  gas  parallel 
to  the  axis  of  the  cylinder,  while  a  velocity  at  right  angles  to  this 
axis  is  imparted  to  them  by  the  electric  field.  Let  CO ',  Fig.  18, 
represent  a  section  of  the  outer  cylinder,  DB  that  of  the  inner  one, 


Fig.  13. 

dbmn  the  beam  of  Rontgen  rays  ionising  the  gas.  If  CC'  is  at 
a  higher  potential  than  DB,  then  a  positive  ion  starting  from 
d  will  move  along  a  curved  path  between  the  cylinders,  finally 
reaching  the  inner  cylinder  at  a  point  K  whose  horizontal  distance 
from  d  is  one  of  the  quantities  measured  in  these  experiments. 
This  distance,  X,  can  easily  be  expressed  in  terms  of  the  velocity  of 
the  ion  under  unit  electric  force.  For  let  b  and  a  be  respectively 
the  radii  of  the  outer  and  inner  cylinders,  A  the  potential  difference 
between  the  cylinders,  then  the  radial  electric  force  R  at  a  distance 
r  from  the  common  axis  of  the  cylinders  is  given  by  the  equation 

R  =        A 

~rloge(6/a); 


26]  WHEN   IN  THE  CONDUCTING  STATE.  43 

thus  if  v  is  the  velocity  of  the  ion  under  unit  electric  force,  then 
on  the  assumption  that  the  velocity  is  proportional  to  the  electric 
force  we  have,  if  V  is  the  radial  velocity  of  the  ion  at  a  distance 
r  from  the  axis  of  the  cylinders, 

V==        Av 

r  log,  (b/a)  ' 

If  u  is  the  velocity  of  the  gas  parallel  to  the  axis  of  the  cylinders 
which  we  shall  take  as  the  axis  of  x,  then  the  differential  equation 
to  the  path  of  the  ion  is 

dx  _  u 
dr      V 

_  loge  (b/a)  ur 
Av 

hence  X  the  horizontal  distance  from  d  at  which  the  ion  strikes 
the  inner  cylinder  is  given  by  the  equation 


rb 

Now  2?r      urdr  is  the  volume  of  gas  which  passes  in  unit  time 

J  a 

between  the  cylinders.     We  shall  denote  this  quantity,  which  is 
easily  measured,  by  Q,  then  we  have 

log.(6/a)« 
~ 


Thus  if  we  know  X  we  can  easily  determine  v.  The  time  T 
taken  by  the  ion  to  pass  from  one  cylinder  to  the  other  is  given 
by  the  equation 


These  equations  apply  to  ions  starting  from  the  inner  surface 
of  the  outer  cylinder.     In  practice  the  production  of  ions  is  not 


44  PROPERTIES   OF   A   GAS  [26 

confined  to  the  surface  of  the  cylinder  but  extends  throughout 
a  layer  db  reaching  from  one  cylinder  to  the  other.  The  ions 
which  start  from  a  point  in  db,  nearer  to  the  surface  of  the  inner 
cylinder  than  d,  will  evidently  not  be  carried  so  far  down  the  tube 
by  the  stream  as  an  ion  starting  from  d.  Thus  the  preceding 
equations  give  us  the  position  of  the  furthest  point  down  the  inner 
cylinder  which  is  reached  by  the  ions.  In  order  to  determine  this 
point  the  inner  cylinder  is  divided  at  K  into  two  parts  insulated 
from  each  other,  the  part  D  to  the  left  being  connected  with  the 
earth,  while  the  part  B  to  the  right  is  connected  with  one  pair  of 
quadrants  of  an  electrometer.  If  a  constant  stream  of  gas  is  sent 
between  the  cylinders,  then  when  the  potential  of  CC'  is  above 
a  certain  value,  all  the  ions  from  the  volume  dd  which  move 
inwards  will  reach  DB  to  the  left  of  K  and  will  not  affect  the 
electrometer.  By  gradually  diminishing  the  potential  of  CC'  we 
reach  a  value  such  that  the  ions  starting  from  the  outer  edge  of 
d  reach  DB  just  to  the  left  of  K\  when  this  stage  is  reached  the 
electrometer  begins  to  be  deflected.  If  then  in  equation  (1)  we 
put  for  A  the  difference  of  potential  corresponding  to  this  stage, 
and  for  X  the  horizontal  distance  of  K  from  d,  we  shall  be  able 
to  deduce  the  value  of  v. 

Corrections.  In  consequence  of  the  diffusion  of  the  ions,  all 
the  ions  starting  from  d  will  not  follow  exactly  the  line  dK,  and  some 
of  the  ions  will  be  found  to  the  right  of  the  line.  The  consequence 
of  this  is  that  the  electrometer  will  begin  to  be  deflected  even  when 
the  potential  difference  A  is  theoretically  sufficient  to  bring  all 
the  ions  to  the  left  of  K\  thus  the  observed  potential  difference 
when  the  deflections  begin  is  slightly  too  large,  and  therefore  the 
values  of  v  determined  by  equation  (1)  are  a  little  too  small. 
Similar  effects  to  those  due  to  diffusion  will  be  produced  by  the 
mutual  repulsion  of  the  ions.  It  is  evident  that  the  magnitude  of 
these  effects  will  depend  upon  the  time  it  takes  the  ion  to  travel 
between  the  cylinders ;  if  this  time  were  zero,  neither  diffusion 
nor  repulsion  would  have  time  to  produce  any  effect,  thus  the 
longer  the  time  taken  by  the  ions  to  travel  between  the  cylinders, 
the  smaller  would  be  the  value  of  v  as  determined  by  this  method. 
The  time  T,  as  we  see  from  equation  (2),  depends  upon  the  velocity 
of  the  air  blast  and  the  strength  of  the  field ;  by  altering  these 
quantities  it  is  possible  to  determine  the  values  of  v  for  a  con- 


26] 


WHEN    IN    THE    CONDUCTING   STATE. 


45 


siderable  range  of  values  of  T  \  the  values  so  found  decrease  as  was 
to  be  expected  slightly  as  T  increases,  the  relation  between  v  and 
T  being  found  by  experiment  to  be  a  linear  one.  Curves  in  which 
the  ordinates  were  the  ionic  velocities  and  the  abscissae  the  time 
T  were  drawn,  and  the  curve  (which  was  found  to  be  a  straight 
line)  prolonged  until  it  cut  the  line  T  =  0;  the  corresponding  value 
of  v  was  taken  as  the  ionic  velocity.  An  example  of  such  curves 
is  given  in  Fig.  14,  the  o's  and  xs  are  the  points  determined  by 


Fig.  u. 

actual  experiments.  The  points  at  which  the  lines  intersect 
the  line  T=0  give  1/48  cm./sec.  for  the  velocity  of  the  negative 
ion  and  1/34  for  the  velocity  of  the  positive,  when  the  potential 
gradient  is  one  volt  per  cm. 

Smaller  corrections  have  to  be  applied  for  the  disturbance  in 
the  electric  field  produced  by  the  presence  of  an  excess  of  ions  of 
one  sign  over  those  of  the  other  in  different  parts  of  the  field.  It 
was  proved  by  direct  experiment  that  the  effects  due  to  surface 
ionisation  were  not  appreciable. 

The  apparatus  used  to  carry  out  this  method  is  represented  in 
section  in  Fig.  15.  A  A'  was  the  outer  cylinder;  it  had  an  internal 
diameter  of  5'1  cm.  and  a  total  length  of  142  cm.  The  parts  to  the 
right  of  V  and  to  the  left  of  V  were  made  of  brass  tubing ;  the 
part  between  W  was  aluminium  tubing  of  the  same  diameter; 
this  piece  was  inserted  so  as  to  permit  the  Rontgen  rays  to  pass 
through.  The  tubes  were  fastened  together  by  airtight  joints  and 
placed  on  insulating  supports. 

The  inner  cylinder  BB'  was  an  aluminium  tube ;  in  one  set  of 
experiments  it  was  1  cm.  in  diameter,  in  another  it  was  2'8  cm. ; 


46 


PROPERTIES   OF   A   GAS 


[26 


the  ends  of  this  tube  were  closed  by  conical  pieces.     The  tube 
was  divided  at  C  and  the  two  portions  separated  by  '5  mm.  and 


Fig.  15. 

insulated  by  ebonite  plugs.  The  tube  was  supported  by  the 
ebonite  rod  Q  and  by  the  stiff  brass  wires  Y  and  Y'  which  passed 
through  ebonite  plugs  in  the  outer  cylinder,  and  served  to  connect 
B'  with  the  earth,  and  B  with  one  pair  of  quadrants  of  the  electro- 
meter. The  electrometer  was  a  very  sensitive  one  giving  a 
deflection  of  500  scale  divisions  for  a  potential  difference  of  one 
volt.  The  narrow  vertical  beam  of  rays  was  adjusted  and  kept 
definite  by  the  slits  in  the  lead  plates  8,  HH'  and  LL'.  A  con- 
stant and  measurable  supply  of  gas  was  sent  through  the  tube  by 
a  gasometer.  Experiments  were  made  with  gases  carefully  dried 
and  with  gases  saturated  with  water  vapour.  Two  series  of  ex- 
periments were  made,  one  with  an  inner  tube  1  cm.  in  diameter, 
the  other  with  an  inner  tube  2*8  cm.  in  diameter ;  the  results 
obtained  in  the  one  series  agreed  very  well  with  those  obtained  in 
the  other. 

The  values  of  the  ionic  velocities  obtained  by  this  method  are 
given  in  the  following  table;  they  have  been  reduced  to  the 
uniform  pressure  of  760  mm.  of  mercury  on  the  assumption  (see 
p.  30)  that  the  ionic  velocity  under  a  given  potential  gradient  is 
inversely  proportional  to  the  pressure. 


27] 


WHEN  IN  THE  CONDUCTING  STATE. 
IONIC  VELOCITIES. 


47 


Gas 

Velocities  in 
under  a  potei 
of  one  vo 

Positive  ions 

cm.  per  sec. 
itial  gradient 
t  per  cm. 

Negative  ions 

Ratio  of 
velocities  of 
negative  and 
positive  ions 

Tempera- 
ture 
degrees 
centigrade 

Air  dry 

1-36 
1-37 
1-36 
1-29 
•76 
•82 
6-70 
5-30 

1-87 
1-51 
1-80 
1-52 
•81 
•75 
7-95 
5-60 

1-375 
1*10 

1-32 
1-18 
1-07 
•915 
1-19 
1-05 

13'5 
14 
17 
16 
17-5 
17 
20 
20 

Air  moist    

Oxygen  dry    

Oxygen  moist     

Carbonic  acid  dry  .  .  . 
Carbonic  acid  moist 
Hydrogen  dry    .... 

Hydrogen  moist    ... 

The  intensity  of  ionisation  was  altered  by  causing  the  Rontgen 
rays  to  pass  through  aluminium  plates  of  different  thicknesses,  the 
ionic  velocities  were  found  to  be  independent  of  the  intensity  of 
the  rays. 

The  results  obtained  by  Zeleny  agree  well  with  those  obtained 
for  the  sum  of  the  velocities  obtained  by  Rutherford  (see  page 
34)  for  air,  oxygen,  and  hydrogen,  allowing  for  the  uncertainty 
as  to  the  amount  of  moisture  in  the  gases  used  by  Rutherford ; 
for  carbonic  acid  however  there  is  considerable  discrepancy,  as 
2*15  cm. /sec.,  the  value  of  the  sum  of  the  velocities  obtained  by 
Rutherford,  is  nearly  40  per  cent,  greater  than  the  value  1'57 
obtained  by  Zeleny,  and  as  Zeleny  found  that  this  sum  was  the 
same  whether  the  gases  were  dry  or  moist  the  discrepancy  cannot 
be  explained  as  due  to  the  excess  or  defect  of  moisture  in  Ruther- 
ford's gases. 

Method  of  determining  the  velocity  by  measuring  the  number 
of  ions  sent  by  a  radial  electric  field  to  the  sides  of  a  tube  of 
given  length  when  traversed  by  a  current  of  gas. 

27.  The  principle  of  this  method  which  has  been  used  by  Ruther- 
ford* to  measure  the  velocities  of  the  ions  produced  by  uranium 
radiation  is  as  follows.  Suppose  that  ionised  air  is  blown  through 
a  tube  along  the  axis  of  which  there  is  a  wire  charged  positively, 

*  Eutherford,  Phil  Mag.  v.  47,  p.  109,  1899. 


48  PROPERTIES    OF   A   GAS  [27 

the  electric  field  around  the  wire  will  drag  the  negative  ions  into 
the  wire  and  thus  rob  the  gas  of  a  certain  proportion  of  these  ions  ; 
the  number  of  these  ions  thus  abstracted  from  the  gas  will  depend 
upon  the  relation  between  the  velocity  of  an  ion  in  the  electric 
field  and  the  velocity  of  the  air  blast  ;  if  the  ionic  velocity  were 
infinitely  greater  than  the  velocity  of  the  blast,  all  the  ions  would 
be  abstracted,  while  if  the  velocity  of  the  blast  were  infinitely 
greater  than  the  ionic  velocity,  they  would  all  escape. 

We  see  from  equation  (2),  page  43,  that  t,  the   time  taken 
by  an  ion  to  reach  the  wire,  is  given  by  the  expression 

r2-a2,       6 
t  =  jA^lo&a  ........................  (1)' 

where  r  is  the  distance  from  the  axis  of  the  tube  of  the  point  from 
which  the  ion  starts,  b  the  internal  radius  of  the  tube,  a  the  ex- 
ternal radius  of  the  wire,  A  the  difference  of  potential  between  the 
wire  and  the  tube  (the  wire  being  at  the  higher  potential),  and  u2 
the  velocity  of  the  negative  ion  under  unit  electric  force.  If  in 
equation  (1)  we  put  t  equal  to  the  time  taken  by  the  air  blast  to 
pass  from  one  end  of  the  tube  to  the  other,  we  see  that  all  the  ions 
whose  distance  from  the  axis  of  the  tube  is  less  than  the  value  of 
•r  given  by  equation  (1)  will  be  dragged  into  the  wire;  hence  if  p  is 
the  ratio  of  the  number  of  ions  dragged  from  the  gas  to  the  whole 
number  of  ions,  we  have,  assuming  that  the  ions  are  uniformly  dis- 
tributed over  the  cross-section  of  the  tube, 


........................... 

The  arrangement  used  by  Rutherford  is  represented  in  Fig.  16. 

A  paper  tube  coated  with  uranium  oxide  was  fitted  into  a 
metal  tube  T  4  cm.  in  diameter.  A  blast  of  air  from  a  gasometer 
after  passing  through  a  plug  of  cotton-  wool  C  to  remove  the  dust 
passed  through  a  long  metal  tube  AB  connected  with  the  earth  ; 
into  this  tube  cylindrical  electrodes  A  and  B  were  fastened  by 
insulating  supports  so  as  to  be  coaxial  with  the  tube.  The  elec- 
trode A  was  charged  up  by  a  battery,  and  the  electrode  B  was 
connected  with  one  pair  of  quadrants  of  an  electrometer.  If  B 


28]  WHEN   IN   THE   CONDUCTING  STATE.  49 

were   charged   initially  to   a  potential  of  the  same  sign   as  A 
(suppose  positive)  large  enough  to  saturate  the  gas,  then  the  rate 


Earth 
Fig.    16. 

of  leak  of  the  electrometer  when  the  air  blast  was  passing  would 
measure  the  number  of  negative  ions  which  escaped  being  dragged 
into  the  electrode  A  ;  by  comparing  the  rate  of  leak  when  the 
electrode  A  is  not  charged  with  the  rate  when  it  is  charged  to  a 
known  potential,  we  can  determine  the  value  of  p  in  equation  (2). 
Rutherford  did  not  use  this  arrangement  to  measure  directly  the 
velocity  of  the  ions  produced  by  the  uranium  radiation,  but  proved 
by  means  of  it  that  the  velocities  of  these  ions  were  the  same  as 
those  of  the  ions  produced  by  Rontgen  rays.  For  this  purpose, 
after  measurements  of  p  had  been  made  with  the  uranium  cylinder 
in  place,  this  cylinder  was  removed  and  replaced  by  an  aluminium 
one  exposed  to  Rontgen  rays,  the  strength  of  these  rays  being 
adjusted  so  that  the  amounts  of  ionisation  in  the  two  cases 
were  approximately  equal ;  measurements  of  p  were  then  made 
with  the  Rontgen  rays  on  and  were  found  to  be  identical  with 
those  obtained  when  the  ionisation  was  produced  by  uranium 
radiation,  thus  proving  that  the  ionic  velocities  are  the  same  in 
the  two  cases. 

28.  A  method  which  is  the  same  in  principle  as  this  was 
first  used  by  McClelland  to  measure  the  velocities  of  the  ions 
produced  by  flames*,  and  by  arcs  and  incandescent  wiresf:  tht 
results  of  these  experiments  showed  that  the  velocity  of  the  ions 
diminishes  very  greatly  when  they  get  into  the  cooler  parts  of  the 
flame,  suggesting  that  there  is  a  rapid  condensation  round  the 
ions  of  some  of  the  products  of  combustion  of  the  flame.  The 

*  McClelland,  Phil.  Mag.  v.  46,  p.  29,  1898. 

t  McClelland,  Proc.  Camb.  Phil.  Soc.  x.  p.  241,  1899. 

T.  G.  * 


50 


PROPERTIES  OF  A  GAS 


[29 


diminution  of  velocity  is  clearly  shown  in  the  following  table  given 
by  McClelland. 


Distance  of  point  where 
velocity  was  measured 
from  the  flame 

Temperature  at  this  point 

Velocity  of  ion  under 
a  force  of  one  volt 
per  centimetre 

5'5  cm. 
10     cm. 
14'5  cm. 

230°  C. 
160°  C. 
105°  C. 

•23  cm.  /sec. 
•21  cm.  /sec. 
•04  cm./sec. 

These  velocities  are  all  of  them  small  compared  with  the  velo- 
cities of  the  ions  produced  by  Rontgen  rays  or  by  radio-active 
substances.  In  the  case  of  the  ions  from  flames  as  in  other  cases 
the  negative  ions  move  faster  than  the  positive.  McClelland 
applied  the  same  method  to  the  determination  of  the  velocities 
of  the  ions  produced  by  arcs  or  incandescent  wires ;  he  found  in 
these  cases  the  same  variability  in  the  velocity  as  he  had  pre- 
viously observed  in  the  ions  from  flames ;  in  the  case  of  the  arcs 
and  wires,  however,  he  found  that  the  hotter  the  flame  or  wire  the 
smaller  the  velocity  of  the  ion.  We  shall  return  to  the  considera- 
tion of  these  phenomena  when  we  discuss  the  electrical  properties 
of  flames  and  arcs. 

Determination  of  the  ionic  velocities  by  means  of  an  alternating 

electric  field. 

29.  This  method,  which  however  can  only  be  applied  when 
we  have  the  ionisation  confined  to  a  thin  layer  of  gas,  and  when 
moreover  all  the  ions  are  of  one  sign,  is  a  very  convenient  and 
accurate  one.  It  was  used  by  Rutherford*  to  determine  the 
velocity  of  the  negative  ions  which  are  produced  close  to  a 
metallic  plate  when  that  plate  is  illuminated  by  ultra-violet  light. 
The  principle  of  the  method  is  as  follows.  AB  (Fig.  17)  is  a, 
horizontal  plate  made  of  well  polished  zinc,  it  is  carefully  insulated, 
and  can  be  moved  vertically  up  and  down  by  means  of  a  screw ; 
it  is  connected  with  one  pair  of  quadrants  of  an  electrometer,, 
whose  other  quadrants  are  connected  with  the  earth.  CD  is  a 
base  plate  with  a  hole  EF  cut  in  it ;  this  hole  is  covered  in  with 

*  Rutherford,  Proc.  Camb.  Phil.  Soc.  ix.  p.  401,  1898. 


29] 


WHEN   IN  THE   CONDUCTING  STATE. 


fine  wire  gauze,  ultra-violet  light  is  sent  through  this  gauze  and 
falls  on  the   plate  AB.     CD  is  connected   with   an  alternating 


current  dynamo  or  any  other  means  of  producing  an  alternating 
difference  of  potential  proportional  to  a  simple  harmonic  func- 
tion of  the  time ;  the  other  pole  of  this  instrument  is  put  to 
earth.  Suppose  now  that  at  any  instant  the  potential  of  CD  is 
higher  than  that  of  AB,  the  negative  ions  at  AB  will  be  attracted 
towards  CD,  and  will  continue  to  move  towards  it  as  long  as  the 
potential  of  CD  is  higher  than  that  of  AB.  If  however  the 
potential  difference  between  CD  and  AB  changes  sign  before  the 
negative  ions  reach  CD  these  ions  will  be  driven  back  to  AB,  sc 
that  this  plate  will  not  lose  any  negative  charge.  AB  will  thus 
not  begin  to  lose  negative  electricity  until  the  distance  between 
the  plates  AB  and  CD  is  less  than  the  distance  passed  over  by 
the  negative  ion  during  the  time  the  potential  of  CD  is  greater 
than  that  of  AB.  The  method  consists  in  altering  the  distance 
between  the  plates  until  AB  just  begins  to  lose  a  negative  charge, 
then  if  we  know  this  distance  and  the  frequency  and  maximum 

4—2 


52 


PROPERTIES   OF   A   GAS 


[29 


value  of  the  potential  difference  we  can  deduce  the  ionic  velocity 
of  the  negative  ion.  For  let  the  potential  difference  between 
CD  and  AB  at  the  time  t  be  equal  to  a  sinpt,  then  if  d  is  equal 
to  the  distance  between  these  plates,  the  electric  force  is  equal  to 
(a/d)  sin  pt,  and  if  u  is  the  velocity  of  the  ion  under  unit  electric 
force,  the  velocity  of  the  negative  ion  in  this  field  will  be 

u  (ajd)  sin  pt  ; 

hence  if  x  is  the  distance  of  the  ion  from  the  plate  AB  at  the 
time  t  we  have 

dx 


or 


ua 


ua 


if  x  =  0  when  t  =  0. 

Thus  the  greatest  distance  the  ion  can  get  from  the  plate  AB 
is  equal  to  2ua/pd.  If  the  distance  between  the  plates  is  gradually 
reduced,  the  plate  AB  will  begin  to  lose  a  negative  charge  when 

2ua  vd2 

d  =  — ,  ,  or  u  —  ~-  . 
pd  2a 

Hence  if  we  measure  p,  a  and  d  we  can  determine  u. 

In  this  way  Rutherford  found  for  the  velocities  under  a 
potential  gradient  of  1  volt  per  cm.  of  the  negative  ion  produced 
by  the  incidence  of  ultra-violet  light  on  a  zinc  plate,  the  following 
values,  for  dry  gases. 


Gas 

Ionic  velocity 

Air  

1  "4   cm  /sec 

Hydrogen    
Carbonic  acid... 

3*9   cm./sec. 

•78  cm./sec. 

These  values  differ  but  little  from  those  obtained  for  Rontgen 
rays. 

Rutherford  found  that  the  velocity  of  the  ions  was  independent 
of  the  metal  of  which  the  plate  AB  was  made :  and  he  proved  by 
this  method  that  the  velocity  of  the  ions  under  a  constant 


30]  WHEN   IN  THE  CONDUCTING  STATE.  53 

potential  gradient  varies  inversely  as  the  pressure,  at  any  rate 
down  to  pressures  of  34  mm.  of  mercury  which  was  the  lowest 
pressure  at  which  he  worked. 


Chattock' 8  method  of  measuring  the  velocities  of  ions  produced  by 
tlie  disdiarye  of  electricity  from  a  sharp  point. 

30.  The  preceding  methods  would  be  very  inconvenient  in 
the  case  when  the  electric  field  is  as  strong  and  the  velocities  of 
the  ions  therefore  as  great  as  they  are  when  electricity  is  dis- 
charging from  a  pointed  conductor.  For  this  case,  in  which  the 
ions  at  some  little  distance  from  the  point  are  all  of  one  sign, 
Chattock*  has  devised  a  very  ingenious  method  by  means  of  which 
he  has  been  able  to  measure  the  velocities  of  these  ions.  The 
principle  of  the  method  is  as  follows.  Let  P  represent  a  vertical 
needle  discharging  electricity  from  its  point  into  the  surrounding 
air ;  consider  the  force  acting  on  the  ions  included  between  two 
horizontal  planes  A  and  B,  Fig.  18.  If  Z  is  the  vertical  corn- 


Fig.  18. 

ponent  of  the  electric  intensity,  p  the  density  of  the  electrification; 
the  resultant  force  F  on  the  ions  included  between  A  and  B  is 
vertical  and  equal  to 


InZpdxdydz. 


If  the  velocity  of  the  ion  under  unit  electric  force  is  u,  then 
w  the  vertical  velocity  of  the  ion  is  equal  to  uZ.     If  all  the  ions 

*  Chattock,  Phil.  Mag.  v.  48,  p.  401,  1899;  Chattock,  Walker  and  Dixon,  Phil. 
Mag.  vi.  1,  p.  79,  1901. 


54  PROPERTIES   OF  A   GAS  [30 

are  of  one  sign  so  that  u  is  the  same  for  all  the  ions,  we  have, 
since  Z  —  w/u, 


F  =  -  \\\wpdxdydz. 


Since  the  ions  are  all  of  one  sign  I  \pwdxdy  is  the  quantity  of 

electricity  streaming  across  a  horizontal  plane  in  unit  time  ;  this  is 
the  same  for  all  horizontal  planes,  and  is  equal  to  i  where  i  is  the 
current  of  electricity  flowing  from  the  needle  point,  hence  we  have 


where  ZB  —  ZA  is  the  vertical  distance  between  the  planes  A  and  B. 
This  force  F  must  be  balanced  by  the  difference  of  the  gaseous 
pressures  over  A  and  B,  hence  if  pB  and  pA  denote  respectively 
the  total  pressures  over  the  planes  A  and  B  we  have 


and  hence  u  =       B~A   ..  .  .  (1). 

PB-PA 

Thus,  by  the  measurement  of  these  pressures  and  of  the 
current  flowing  from  the  point  (the  latter  measurement  is  easily 
made  by  inserting  a  galvanometer  in  series  with  the  needle  point), 
we  can  deduce  the  value  of  u. 

The  apparatus  used  by  Chattock  to  carry  out  this  method  is 
represented  in  Fig.  19.  The  discharging  needle  is  supported  in  a 


(Zero  of  2) 


Fig.  19. 

narrow  sliding  glass  tube  drawn  out  at  the  end  B ;  it  discharges  to 
a  ring  A  made  of  smooth  metal ;  the  needle  and  ring  are  enclosed 
in  a  wide  glass  tube  E,  the  ends  of  which  are  connected  by  tubes 
T!  and  T2  with  the  ends  of  a  U  tube  pressure  gauge  containing 


30]  WHEN   IN  THE  CONDUCTING  STATE.  55 

water  ;  the  ring  A  can  be  moved  along  the  tube  by  means  of  a 
screw.  In  this  apparatus,  since  there  is  no  current  to  the  left  of 
the  ring  or  to  the  right  of  the  point,  if  we  put  ZB  -  ZA  equal  to  the 
distance  of  the  point  from  the  ring,  and  if  o>  is  the  difference 
of  pressure  in  dynes  per  sq.  cm.  measured  by  the  pressure  gauge, 
A  the  area  of  cross-section  of  the  tube,  then 


where  p'  is  the  part  of  the  pressure  which  is  borne  by  the  ring. 
We  have,  by  equation  (1), 


It  was  assumed  that  when  the  point  was  a  considerable  .distance 
from  the  ring  p'  became  independent  of  z  ;  on  this  supposition  we 
have,  if  Aw,  kz  are  corresponding  changes  in  w  and  zt 


and  it  was  from  this  relation  that  u  was  calculated.  Chattock 
found  for  the  velocities  of  the  negative  and  positive  ions  in  air 
under  a  potential  gradient  of  a  volt  per  cm.  the  values  1'8  cm./see. 
and  T38  cm./sec.,  which  agree  well  with  those  found  for  the  ions 
produced  by  Rontgen  rays,  and  we  conclude  that  the  ions  in  the 
two  cases  are  the  same.  In  the  second  paper  Chattock  extends 
the  method  to  hydrogen,  oxygen,  and  carbonic  acid  as  well  as  air, 
and  again  finds  close  agreement  between  the  velocities  of  the  ions 
produced  by  the  point  discharge  and  those  produced  by  radio- 
active substances.  He  points  out  that  while  the  determination  of 
the  ionic  velocities  of  the  positive  ions  showed  in  all  gases  great 
consistency,  considerable  variations  which  could  not  be  attributed 
to  errors  of  experiment  were  found  in  the  values  of  the  velocities 
of  the  negative  ions.  This  was  especially  the  case  in  hydrogen, 
where  the  values  of  the  ionic  velocity  of  the  negative  ion  varied 
from  6*8  to  8*5  ;  in  the  other  gases  the  variation  is  not  so  marked. 
Chattock  ascribes  this  variation  to  the  gases  occluded  by  the 
discharging  point  ;  when  this  point  is  negative  some  of  these 
occluded  gases  are  given  off  and  help  to  carry  the  discharge,  and 
as  the  velocity  of  the  hydrogen  ions  is  very  large  compared  with 
that  of  other  ions,  it  is  urged  that  a  small  admixture  of  other  and 
more  slowly  moving  ions  might  produce  a  considerable  lowering 


56 


PKOPERTIES  OF  A  GAS 


[31 


of  the  average  velocity.  When  the  point  is  positive  the  occluded 
gas  is  supposed  either  not  to  be  given  off,  or,  if  given  off,  not 
to  take  any  part  in  carrying  the  discharge.  This  explanation  is 
consistent  with  other  phenomena  connected  with  the  discharge  of 
electricity  from  metals ;  we  shall  see  that  in  the  electric  discharge 
through  gas  at  low  pressures  occluded  gas  is  given  off  from  the 
cathode,  and  that  the  amount  of  gas  so  given  off  has  very  con- 
siderable influence  upon  the  phenomena.  The  values  obtained  by 
Chattock  for  the  velocities  of  the  ions  produced  by  the  point 
discharge  are  given  in  the  following  table,  in  which  V+  denotes 
the  velocity  of  the  positive  ion,  F_  that  of  the  negative,  and  V  the 
mean  of  these  velocities.  The  gases  were  dry. 


Gas 

V+ 

V_ 

V 

F_/F+ 

Hydrogen 

5  '4 

7-43 

6-41 

1-38 

Carbonic  acid    ... 
Air  

0-83 
1-32 

0-925 
1-80 

0-88 
1-55 

I'll 

1-36 

Oxygen  ., 

1-30 

1-85 

1-57 

1-42 

Charges  on  the  ions. 

31.  We  saw  on  page  32  that  the  coefficient  of  diffusion  D  of 
an  ion  through  a  gas  was  connected  with  the  velocity  u  of  the 
same  ion  through  the  same  gas  under  unit  electric  force  by  the 
equation 

u      Ne 


where  N  is  the  number  of  molecules  in  a  c.c.  of  gas  at  a 
pressure  of  II  dynes  per  square  cm.  It  is  to  be  remembered 
that  this  relation  is  obtained  on  the  supposition  that  a  number 
of  ions  in  a  given  volume  produce  the  same  pressure  as  the  same 
number  of  molecules  of  a  perfect  gas  at  the  same  temperature  ;  in 
other  words,  that  the  ions  behave  like  a  perfect  gas  with  respect  to 
pressure.  As  we  have  seen  that  the  ions  in  a  gas  at  atmospheric 
pressure  are  probably  aggregations  of  considerable  complexity  as 
compared  with  the  molecules  of  a  perfect  gas,  we  must  regard  this 
assumption  as  only  an  approximation  to  the  truth,  and  one  which 
would  cease  to  be  even  that  when  the  ions  are  as  large  as  those  which 
occur  in  the  colder  parts  of  flames  or  near  an  incandescent  wire. 


31] 


WHEN   IN   THE   CONDUCTING  STATE. 


57 


Taking  the  values  of  D  given  by  Townsend  and  (1)  the  values 
of  u  given  by  Eutherford,  (2)  those  given  by  Zeleny,  we  get  the 
following  values  for  Ne  x  lO"10,  e  being  expressed  in  electrostatic 
units. 

From  Rutherford's  experiments  on  the  mean  velocities  of  the 
ions  in  gases,  and  the  mean  of  the  coefficients  of  diffusion  given  by 
Townsend  we  get 

I. 


Gas 

Ne  x  10-10 

Air 

1-35 

Oxygen 

1-25 

Carbonic  acid... 
Hydrogen    

1-30 
1-00 

From  Zeleny 's  values  for  the  velocities  of  the  ions  and  Townsend's 
for  the  coefficients  of  diffusion  we  get 

II. 


Moisl 

;  Gas 

Dry 

Gas 

Gas 

Positive  ions 

Negative  ions 

Positive  ions 

Negative  ions 

Air  

1-28 

1-29 

1-46 

1-31 

Oxygen 

1-34 

1-27 

1-63 

1-36 

Carbonic  acid  
Hydrogen    

1-01 
1-24 

•87 
1-18 

•99 
1-63 

•93 
1-25 

Since  one  electromagnetic  unit  or  3  x  1010  electrostatic  units 
of  electricity  when  passing  through  acidulated  water  liberates 
1*23  c.c.  of  hydrogen  at  the  temperature  of  15°  C.  and  pressure  of 
760  mm.  of  mercury,  and  since  in  T23  c.c.  of  gas  there  are  2'46AT 
atoms  of  hydrogen,  we  have,  if  E  is  the  charge  in  electrostatic 
units  on  the  atom  of  hydrogen  in  the  electrolysis  of  solutions, 
2'4>6NE  =  3  xlO10, 


or 


The  mean  of  all  the  values  of  Ne  in  Tables  I  and  II.  is  T24  x  1010. 


58  PROPERTIES   OF  A  GAS  [32 

We  conclude  then  (1)  that  the  charges  carried  by  the  gaseous 
ions  are  the  same  whether  the  ions  are  produced  in  air,  oxygen, 
hydrogen  or  carbonic  acid,  (2)  that  this  charge  is  equal  to  the 
charge  carried  by  the  hydrogen  atom  in  the  electrolysis  of 
solutions. 

The  proof  of  the  equality  of  the  charges  on  the  ions  in  dif- 
ferent gases  was  first  obtained  by  the  author  by  direct  measure- 
ments of  the  charges  carried  by  the  gaseous  ions.  Though  the 
variations  in  the  value  of  Ne  given  in  Tables  I.  and  II.  are  greater 
than  we  should  have  expected  from  the  accuracy  with  which  the 
experiments  were  made,  they  are  not  sufficiently  regular  to  enable 
us  to  draw  any  conclusions ;  thus  for  example  in  Table  I.  Ne  for 
carbonic  acid  is  considerably  greater  than  for  hydrogen,  while  in 
Table  II.  it  is  very  much  less.  We  must  remember  too  that  these 
results  have  been  obtained  on  the  supposition  that  the  complex 
ions  behave  like  a  perfect  gas ;  if  they  behaved  like  complex 
vapours  the  values  obtained  on  this  supposition  would  be  some- 
what too  large. 


Currents  in  the  gas  caused  by  the  motion  of  ions  through  it. 

32.  Since  the  charged  ions  when  in  an  electric  field  settle 
down  to  a  state  of  steady  motion  in  which  they  have  no  accelera- 
tion the  force  exerted  by  the  field  on  the  ions  is  transferred  to  the 
gas.  Thus  when  in  any  region  there  is  an  excess  of  the  ions  with 
charges  of  one  sign  over  those  having  the  opposite  sign  there  will 
be  a  resultant  force  acting  on  the  gas  in  this  region  which  may 
start  currents  in  the  gas.  Thus  to  take  the  case  of  a  current 
passing  through  ionised  gas  between  parallel  metal  plates,  there 
is,  as  we  shall  see  in  the  next  paragraph,  an  excess  of  positive  ions 
in  the  layer  of  gas  near  the  negative  plate  and  of  negative  ions  in 
the  layer  next  the  positive  plate ;  thus  these  layers  will  be  acted 
on  by  forces  tending  to  make  them  move  towards  their  respective 
plates.  If  these  plates  were  infinite  these  forces  would  be  balanced 
by  an  excess  of  pressure  next  the  plate,  but  if  the  plates  are  finite 
this  excess  of  pressure  will  relieve  itself  by  the  gas  moving  round 
to  the  back  of  the  plate  and  a  system  of  air  currents  will  be 
set  up. 


32] 


WHEN   IN  THE   CONDUCTING  STATE. 


59 


These  currents  have  been  observed  by  Zeleny*  by  means  of 
the  apparatus  represented  in  Fig.  20.  A  and  B  are  the  two 
parallel  metal  plates,  connected  to  the  opposite  poles  of  a  battery 
of  storage  cells.  The  plates  are  enclosed  in  a  box  of  which  the 


Fig.  20. 

sides  P  and  Pr  are  made  of  blocks  of  paraffin,  while  the  other 
two  sides  are  glass  to  enable  the  observer  to  see  what  is  going  on 
inside.  The  bottom  of  the  box  is  made  of  wood,  Rontgen  rays 
pass  through  this  and  ionise  the  gas  between  the  plates.  The 
vessel  R  contains  liquid  ammonia,  from  which  ammonia  gas  passes 
through  the  tube  S  into  the  box.  The  tubes  T  and  T'  contain  drops 
of  hydrochloric  acid.  The  particles  of  ammonium  chloride  formed 
at  the  lower  ends  of  the  tube,  where  the  acid  is  in  contact  with 
the  ammonia,  fall  slowly,  producing  well-defined  vertical  whitish 
streams  a  and  b  near  the  plates  A  and  B.  These  streams  are 
vertical  so  long  as  the  Rontgen  rays  and  the  electric  field  are  not 
on  together.  If,  however,  when  the  electric  field  is  on,  the  gas  is 
exposed  to  the  rays,  the  streams  are  deflected  towards  the  plates 
as  indicated  by  the  dotted  lines  in  the  figure.  In  order  to  show 
that  this  was  not  due  to  any  charge  on  the  solid  particles  of 
ammonium  chloride  the  experiment  was  repeated  with  streams 
of  carbonic  acid  gas,  the  difference  of  refractive  index  between 
this  gas  and  air  being  sufficient  to  render  the  streams  visible ;  it 
was  found  that  these  streams,  like  those  of  the  ammonium  chloride, 
were  deflected  towards  the  plate. 

*  Zeleny,  Proc.  Camb.  Phil.  Soc.  x.  p.  14,  1898. 


60 


PROPERTIES   OF  A   GAS 


[33 


33.  For  convenience  of  reference  we  give  a  table  containing 
the  results  of  the  measurements  of  the  ionic  velocities  made  up 
to  1902.  The  velocities  are  expressed  in  cms.  per  second  and  are 
for  a  potential  gradient  of  1  volt  per  cm.  F+,  F_,  denote  respec- 
tively the  velocities  of  the  positive  and  of  the  negative  ions,  V  the 
mean  of  these  velocities. 

VELOCITIES  OF  IONS. 
Ions  from  Rontgen  Rays. 


Gas 

v+ 

V_ 

V 

Observer 

r  Air  

1-6 

Eutherford 

\  Air  dry 

1-36 

1-87 

1-61 

Zeleny 

Air  moist    

1-37 

1-51 

1-44 

Zeleny 

(  Oxygen    . 

1-4 

Rutherford 

<  Oxygen  dry...         

1-36 

1-80 

1-58 

Zeleuy 

(  Oxygen  moist 

1-29 

1-52 

1-405 

Zeleny 

(  Carbonic  acid  

1-07 

Rutherford 

<  Carbonic  acid  dry  

•76 

•81 

•78 

Zeleny 

(  Carbonic  acid  moist  .  .  . 
(  Hyc^roo'en 

•82 

•75 

•78 
5 

Zeleny 
Rutherford 

<  Hydrogen  dry    . 

6'70 

7-95 

7-2 

Zeleny 

(  Hydrogen  moist     
Nitrogen  

5-30 

5-60 

5-45 
1-6 

Zeleny 
Rutherford 

Sulphur  dioxide  

•5 

Rutherford 

Hydrochloric  acid  
Chlorine  ... 

... 

... 

1-27 
1-0 

Rutherford 
Rutherford 

Ions  from   Ultra-  Violet  Light. 


Ions  from  Flames. 
Velocities  varying  from  -04  to  '23   

Ions  from  point  discharge. 


Air  

1-4 

Rutherford 

Hydrogen   

3-9 

Rutherford 

Carbonic  acid 

•78 

Rutherford 

McClelland 


Hydrogen 

5-4 

7-43 

6'41 

Chattock 

Carbonic  acid  

0-83 

0-925 

0-88 

Chattock 

Air  

1-32 

1-80 

1-55 

Chattock 

Oxygen 

1-30 

1-85 

1-57 

Chattock 

34]  WHEN   IN   THE   CONDUCTING  STATE.  61 


Potential  gradient  between  two  parallel  plates  immersed  in 
an  ionised  gas  and  maintained  at  different  potentials. 

34.  It  was  shown  first  by  Zeleny*,  and  then  independently  by 
Child  f,  that  when  electricity  is  passing  between  two  plates  im- 
mersed in  ionised  gas,  the  potential  gradient  between  the  plates 
is  not  uniform,  but  is  greatest  in  the  neighbourhood  of  the 
electrodes.  The  difference  of  potential  between  one  of  the  plates 
and  any  point  in  the  gas  may  be  measured  by  having  a  water  or 
mercury  dropper  at  the  point ;  the  most  convenient  way,  however, 
is  to  place  at  the  point  a  fine  wire,  which  will  ultimately  assume 
the  potential  of  the  point.  When  the  wire  is  used  it  is  necessary 
however  to  take  several  precautions :  in  the  first  place,  if  the 
number  of  ions  in  the  gas  is  small,  the  wire  will  only  take  up  the 
potential  very  slowly,  and  it  is  important  that  the  instrument 
used  for  measuring  the  capacity  of  the  wire  should  have  very 
small  capacity.  This  circumstance  often  makes  it  desirable  to 
measure  the  potential  of  the  wire  by  means  of  a  small  gold  leaf 
electroscope  instead  of  a  quadrant  electrometer,  which  though 
more  sensitive  to  differences  of  potential  has  yet  a  very  much 
greater  capacity.  Another  point  to  be  remembered  is  that  if  a 
wire  is  placed  in  a  region  where  the  ions  are  all  of  one  sign,  its 
potential  can  only  change  one  way.  Thus  if  it  is  a  region  where 
there  are  only  positive  ions,  its  potential  can  increase  but  cannot 
decrease,  and  thus  if  the  potential  of  the  wire  gets  by  some 
accident  too  high,  it  cannot  sink  to  its  true  value. 

A  characteristic  curve  for  the  distribution  of  potential  between 
the  plates,  due  to  Zeleny,  is  given  in  Fig.  21.  It  will  be  seen 
that  the  gradient  near  the  centre  of  the  field  is  uniform,  but  that 
near  the  plates  the  gradients  get  much  steeper  and  that  they  are 
steeper  at  the  negative  than  at  the  positive  plate. 

d'2V 

From  the  equation    ,—  =  -  4-7T/5,  where  V  is  the  potential  at  a 
ax" 

distance  x  from  the  plate  and  p  the  density  of  the  electrification, 

*  Zeleny,  Phil.  Mag.  v.  46,  p.  120,  1898. 
t  Child,  Wied.  Ann.  Ixv.  p.  152,  1898. 


62 


PROPERTIES  OF  A  GAS 


[34 


we  caD,  if  we  know  the  distribution  of  potential,  calculate  the 
density  of  the  electrification  at  any  point  between  the  plates. 


Drs 


IPO    ^ 


tances 


\. 


\ 


Fig.  21. 

The  density  corresponding  to  the  potential  curve  in  Fig.  21  is 
shown  in  Fig.  22. 


/v, 


gat/ 


Plat 


Po. 


Pizte 


jti  ve 


Fig.  22. 


We  see  that  next  the  positive  plate   there  is  an  excess  of 


34]  WHEN   IN   THE   CONDUCTING   STATE.  63 

* 

negative  electricity  and  an  excess  of  positive  near  the  negative 
plate.  With  the  small  potential  differences  used  in  this  experiment 
the  regions  where  there  is  an  excess  of  one  kind  of  electricity  over 
the  other  are  in  the  immediate  neighbourhood  of  the  plates,  the 
density  of  the  free  electricity  being  exceeding  small  in  the  central 
portion  of  the  field.  If  a  larger  potential  difference  had  been 
applied  to  the  plates,  the  regions  of  free  electricity  would  have 
expanded,  and  with  very  large  potential  differences  these  regions 
would  fill  the  whole  of  the  space  between  the  plates.  In  the 
example  given,  the  greatest  density  of  the  electrification  is  about 
2  x  10~4  electrostatic  units ;  as  the  charge  on  an  ion  is  about 
3'5  x  10~10  such  units  the  number  of  positive  ions  in  a  cubic  centi- 
metre would  exceed  that  of  negative  by  about  6  x  105.  Taking 
the  number  of  molecules  in  a  cubic  centimetre  of  the  gas  as 
3'5  x  1019,  the  ratio  of  the  excess  of  ions  of  one  sign  to  the  number 
of  molecules  is  only  1'6  x  10~14.  As  most  of  the  negative  ions 
would  be  driven  away  from  the  negative  plate,  this  will  approxi- 
mately represent  the  ratio  of  the  number  of  free  ions  to  the 
number  of  molecules,  and  from  it  we  learn  what  a  very  small 
amount  of  ionisation  is  sufficient  to  account  for  many  of  the 
phenomena  of  the  conduction  of  electricity  through  gases. 


CHAPTER  III. 

MATHEMATICAL    THEORY    OF    THE    CONDUCTION    OF 
ELECTRICITY  THROUGH  A  GAS  CONTAINING  IONS. 

35.  WE  shall  now  proceed  to  develop  the  theory  of  electric 
conduction  through  an  ionised  gas  on  the  basis  that  the  velocities 
of  the  ions  are  proportional  to  the  electric  force  acting  upon  them. 
We  shall  take  the  case  of  two  infinite  parallel  metal  plates  main- 
tained at  different  potentials  and  immersed  in  an  ionised  gas;  the 
lines  of  electric  force  are  everywhere  at  right  angles  to  the  plates ; 
they  are  thus  always  parallel  to  a  line  which  we  shall  take  as  the 
axis  of  x. 

Let  nlt  ?i2  be  respectively  the  number  of  positive  and  negative 
ions  per  unit  volume  at  a  place  fixed  by  the  coordinate  x,  let  q 
be  the  number  of  positive  or  negative  ions  produced  in  unit  time 
per  unit  volume  at  this  point  by  the  ionising  agent;  let  X  be 
the  electric  intensity  at  this  point,  R1}  R2  the  velocities  of  the 
positive  and  negative  ions  under  unit  electric  intensity,  so  that 
the  velocities  of  these  ions  at  this  point  are  respectively  R^X, 
R2X ;  let  e  be  the  charge  on  an  ion.  The  volume  density  of  the 
electrification,  supposed  due  entirely  to  the  presence  of  the  ions, 
is  (rij  —  n2)  e ;  hence  we  have 

—  =  4?r  O,  -  n2)  e (1). 

If  i  is  the  current  through  unit  area  of  the  gas,  and  if  we 
neglect  any  motion  of  the  ions  except  that  caused  by  the  electric 
field,  we  have 

i (2). 


35]          MATHEMATICAL   THEORY   OF  THE   CONDUCTION,   ETC.  65 

From  equations  (1)  and  (2)  we  get 
1 


dX 


If  we  measure  the  distribution  of  electric  force  between  the 
plates,  we  can  from  these  equations,  if  we  know  Rl  and  R2,  deter- 
mine H!  and  n2,  or  if  in  addition  to  the  distribution  of  electric 
force,  we  measure,  by  the  methods  previously  given,  n1}  nz  at 
various  points  in  the  field,  we  can  use  these  equations  to  deter- 
mine Rl  and  R^,  the  velocities  of  the  ions. 

When  the  gas  is  in  a  steady  state,  the  number  of  negative  and 
of  positive  ions  in  each  unit  of  volume  must  remain  constant  with 
respect  to  the  time,  thus  the  loss  of  these  ions  must  be  balanced 
by  the  gains.  Now  ions  are  lost  in  consequence  of  the  recom- 
bination of  the  positive  and  negative  ions  :  these  ions  will  come 
into  collision  with  each  other,  and  a  certain  fraction  of  the  whole 
number  of  collisions  will  result  in  the  positive  and  negative  ions 
combining  to  form  a  single  system  which  is  electrically  neutral 
and  which  no  longer  acts  as  an  ion  ;  the  number  of  collisions  in 
unit  volume  in  unit  time  is  proportional  to  n^n^.  We  shall  sup- 
pose that  the  number  of  positive  or  negative  ions  which  recombine 
in  unit  volume  in  unit  time  is  an^n*  :  this  is  the  rate  at  which  unit 
volume  is  losing  positive  and  negative  ions  in  consequence  of 
recombination  ;  in  consequence  of  ionisation  it  is  gaining  them  at 
the  rate  q,  and  in  consequence  of  the  motion  of  the  ions  it  is  losing 

positive  ions  at  the  rate  ^-(n-^R^)  and  negative  ones  at  the  rate 
dec 

—  -=-  (n2R2X):  hence  when  the  gas  is  in  a  steady  state  we  have 
dx 

-T-  (n^X)  =  q  —  an^  ..................  (5), 

(6). 


If  R1  and  Rz  are  constant  at  all  parts  of  the  field,  we  have 
from  (1),  (5)  and  (6) 


T.  G. 


66      MATHEMATICAL  THEORY  OF  THE  CONDUCTION  OF     [35 

From  this  equation,  if  we  measure  the  distribution  of  X2 
between  the  plates,  we  can  determine  whether  ionisation  or  re- 
combination is  in  excess  at  any  point,  for  from  (7)  q  —  cm-^n^  and 
d*X*/dx2  have  the  same  sign,  hence  when  ionisation  is  in  excess  of 
recombination,  i.e.  when  q  —  cm-^n^  is  positive,  d2X2/dx2  is  positive 
and  the  curve  whose  ordinate  is  Xz  is  convex  to  the  axis  of  x  ;  when 
recombination  is  in  excess  of  ionisation  the  curve  for  X2  is  concave 
to  the  axis  of  x. 

Substituting  in  equation  (7)  the  values  of  nlt  n2  given  by 
equations  (3)  and  (4)  we  get 

d*X*  /_!_     _l_ 

'6 


fir*  ~  V7?        7?  /  P      f>*X*(~R 

{*&  X^l         *«2/    \  V  J\.     \J-^i 

x  I i+  ^     ,-     I  U  — 


I  have  not  been  able  to  get  a  general  solution  of  this  differential 
equation  except  when  q  is  constant  and  R^  =  R2  ;  in  that  case  put- 

ting X2  =  y  and  ~  =p  we  get,  writing  R  for  either  R:  or  R2, 
dp 


Integrating  this  we  get 


where  C  is  a  constant  of  integration.  From  this  equation  we  can 
find  the  ratio  of  XQ,  the  electric  intensity  midway  between  the 
plates,  to  X1}  the  electric  intensity  close  to  a  plate.  For  when 
^  =  jR2  the  distribution  of  electric  force  is  symmetrical  and  mid- 
way between  the  plates  dXjdx  and  p  =  0  ;  let  us  further  assume 
that  we  are  dealing  with  a  case  like  that  in  Fig.  22,  where  there  is 
no  free  electricity  for  some  distance  from  the  middle  of  the  plate,  so 
that  here  d2X/dx2  also  vanishes  ;  hence  from  (9)  and  (10)  we  have 

X--.J5L. 

' 


(11). 


35]  ELECTRICITY  THROUGH   A   GAS   CONTAINING  IONS.  67 

Now  at  the  positive  plate  %  =  0  and  at  the  negative  plate 
n2  =  0  ;  hence  at  either  plate  n^n^  =  0,  but 


hence  if  Xt  is  the  value  of  X  at  either  plate,  we  have 

=  CXf^  .......  .  .............  (12). 

SvreR 

Hence  by  (11)  and  (12) 


a 
or  writing  /3  for  SirRe/a.  we  get 


We  see  from  this  equation  that  X0/X1  is  never  greater  than 

<3 

unity  since  /S1^  diminishes  from  unity  to  zero  as  ft  increases 
from  ft  =  0  to  jB  =  infinity.  Since  ft  does  not  involve  either  q  or  i, 
the  ratio  of  the  electric  intensities  does  not  depend  upon  either 
the  intensity  of  the  ionisation  or  of  the  current  between  the  plates. 
For  air  at  atmospheric  pressure  R  =  480  (since  unit  electrostatic 
force  is  300  volts  per  centimetre),  a  is  about  1*2  x  10~6,  (see  page 
19),  and  e  =  3'5  x  10~10;  substituting  these  values  we  find  ft  =  3'9 
for  air  at  atmospheric  pressure.  Since  R  is  inversely  proportional 
to  the  pressure,  /3  is  inversely  proportional  to  the  pressure,  and 
thus  is  very  large  at  the  pressure  of  a  few  millimetres  of  mercury. 
Putting  /3  =  4  we  find 

"V 

-^  =  4*  =  2'51  approximately. 

^-0 

At  low  pressures  j3  is  large,  in  this  case  Xi/Xo^/3*  approx1'- 
mately,  and  thus  the  ratio  of  X1  to  XQ  varies  inversely  as  the 
square  root  of  the  pressure. 

The  experiments  we  have  described  on  the  distribution  of 
electric  force  between  the  plates  show  that  when  the  current  is 
small,  the  regions  where  X  differs  appreciably  from  X0  are  con- 
fined to  two  layers  near  the  plates,  the  distribution  of  X  between 
the  plates  being  represented  by  a  curve  like  that  shown  in  Fig.  23. 

5—2 


68  MATHEMATICAL  THEORY  OF  THE   CONDUCTION  OF  [36 

We  can  very  easily  find  an  inferior  limit  to  X  the  thickness  of  one 
of  these  layers.     For  let  P  be  a  point  on  the  boundary  of  the 


Fig.  23. 

layer  next  the  electrode,  then  since  X  becomes  constant  at  P, 
there  are  as  many  positive  as  negative  ions  in  this  region  and  if 
the  velocities  of  the  ions  are  the  same,  half  the  current  must  be 
carried  by  the  positive  and  half  by  the  negative  ions.  Thus  if  i 
is  the  current  through  unit  area,  and  e  the  charge  on  an  ion,  i/2e 
positive  ions  must  cross  unit  area  of  a  plane  through  P  in  unit 
time  ;  and  all  these  positive  ions  must  be  produced  in  the  region 
between  P  and  the  positive  plate.  But  if  X  is  the  thickness  of  the 
layer,  the  number  of  positive  ions  produced  in  unit  time  corre- 
sponding to  each  unit  area  of  the  plate  is  q\,  the  number  that 
cross  unit  area  at  P  cannot  therefore  be  greater  than  q\,  and 
can  only  be  as  great  when  there  is  no  recombination  of  the  ions 
between  P  and  the  positive  plate,  hence 


or  X  >  i/2eq  ;  thus  i/2eq  is  an  inferior  limit  to  X.  If  /  is  the 
maximum  current,  I  the  distance  between  the  plates,  I  —  qle\ 
hence  i/2I  is  an  inferior  limit  to  \/l. 

36.  Though  we  cannot  find  a  general  solution  of  the  equations 
(1),  (2),  (5),  (6)  when  J^  is  not  equal  to  R2,  we  see  at  once  that 
a  particular  solution  of  these  equations  is  given  by  the  relations 


R 


X-l- 


36]  ELECTRICITY   THROUGH   A   GAS   CONTAINING  IONS.  69 

This  solution  corresponds  to  a  constant  value  of  the  electric 
force  between  the  plates,  and  indicates  that  the  proportion  of  the 
current  carried  by  the  positive  and  negative  ions  respectively  is 
the  same  as  the  ratio  of  the  velocities  of  these  ions.  This  solution 
though  it  may  apply  to  the  central  portion  of  the  field,  cannot 
however  hold  right  up  to  the  plates.  For  suppose  P  is  a  point 
between  the  plates  at  which  this  solution  applies.  Then  across 
unit  area  at  P,  iRij(Ri  +  R*)  e  positive  ions  pass  in  unit  time,  and 
these  must  come  from  the  region  between  P  and  the  positive 
plate  ;  if  the  distance  of  P  from  this  plate  is  X  this  region  cannot 
furnish  more  than  qX  positive  ions  in  unit  time,  and  can  only  do 
this  when  there  is  no  recombination  ;  hence  the  preceding  solution 
cannot  hold  at  a  distance  from  the  positive  plate  less  than 


Similarly  it  cannot  hold  at  a  distance  from  the  negative  plate  less 
than 


We  shall  assume  that  the  preceding  solution  does  hold  at  distances 
from  the  plates  greater  than  the  preceding  values:  and  further 
that  in  the  layers  in  which  the  solution  does  not  hold  there  is  no 
recombination  of  the  ions. 

Let  us  consider  the  state  of  things  at  the  positive  plate  between 
x  —  0  and  x  —  \  ,  where 


Then,  since  in  this  region  there  is  no  recombination,  equations  (1), 

(5),  (6)  become 

dX 

-=-  =  4?r  (??!  -  n2), 

ax 

5  <*«.*>-* 


If  q  is  constant  we  have 


70  MATHEMATICAL  THEORY  OF  THE  CONDUCTION   OF  [36 

where  the  constant  of  integration  has  been  chosen  so  as  to  make 
7^  =  0  when  x=0:  substituting  these  values  for  nl}  n2  in  the 
equation  giving  dXjdx  we  get 

dX  (     fl       1 


vdX      .       (     (I       l\       i  } 

X  -T-  =  4-Tre  \qx  (^  +  ^ }-  -^  [  , 
dx  I1    \Rl     RJ     eR2] 

or  Z2  =  87re  L  ^2  f^r  + -^ )  -  ^ [  +C (13), 


where  (7  is  a  constant  which  may  be  determined  from  the  condition 
that  when  x  =  Xj 


from  this  we  find 


a. 


RI 


C  is  the  value  of  X2  when  x=  0,  i.e.  at  the  positive  plate;  if  we 
call  this  value  Xlt  and  if  XQ  is  the  constant  value  of  X  between 
the  layers,  we  have 

j.  4?n?  Rl  (Tt  j  p  ^li• 

+-    -    p-^  +  ^jjf  , 
O.     M3  ) 

thus  JTj  is  always  greater  than  X0  and  the  ratio  XJXo  does  not 
depend  upon  the  amount  of  ionisation  or  the  strength  of  the 
current  between  the  plates. 

If  Xz  is  the  value  of  X  at  the  negative  plate,  we  can  prove  in 
a  similar  way  that 


Thus  if  1^2,  the  velocity  of  the  negative  ion,  is  very  large  compared 
with  Rly  the  velocity  of  the  positive  ion,  the  value  of  X  at  the 
negative  plate  is  large  compared  with  its  value  at  the  positive, 
and  the  thickness  of  the  layer  in  which  X  is  variable,  is  greater  at 
the  negative  than  it  is  at  the  positive  plate.  A  curve  representing 
the  distribution  of  electric  intensity  between  the  plates  in  this 
case  is  represented  in  Fig.  24. 

If  we  put 


a      4>7re  Rl    „       p  2 

Pi  =  -—  p-  (-#1  +  -#2)  :  P2  =  -  -  -=- 

CL     jfl-2  OL      £ll 


V 


36]  ELECTRICITY  THROUGH   A  GAS  CONTAINING   IONS.  71 

we  have 


when  &  and  /92  are  large  we  have  approximately 


Fig.  24. 

In  the  special  case  when  the  velocities  of  the  positive  and 
negative  ions  are  equal  &  =  /32  and  X^X^  —  (S-n-eR/a.)^,  this  agrees 
when  13  is  large  with  the  result  found  by  the  independent  investi- 
gation of  this  case  given  on  p.  67. 

The  fall  of  potential  Vl  across  the  layer  next  the  positive  plate 
whose  thickness  is  Xj  is  equal  to 

lXdx; 

substituting  the  value  of  X  given  by  equation  (13)  and  integrat- 
ing we  find 


+ 


log 


Since 


-r ,  and  \!  = 


Thus  the  fall  of  potential  across  this  layer  is  proportional  to 
the  square  of  the  current. 


72      MATHEMATICAL  THEORY  OF  THE  CONDUCTION  OF     [37 

If  F2  is  the  change  in  potential  in  crossing  the  layer  next  the 
negative  electrode  we  find  similarly 


If  /:?!  and  /32  are  very  large  we  have  approximately 


Substituting  the  values  of  ftlt  /92  we  find 


or  the  falls  of  potential  at  the  positive  and  negative  plates  are 
proportional  to  the  squares  of  the  velocities  of  the  positive  and 
negative  ions. 

Let  us  consider  how  the  fall  of  potential  varies  with  the 
pressure  of  the  gas  :  if  p  is  the  pressure,  Rl  and  R2  are  inversely 
proportional  to  p,  and  q  is  directly  proportional  to  p,  hence  we  see 
that  for  a  given  current  Vl  and  F2  vary  inversely  as  p. 

37.  The  relation  between  the  potential  difference  between  the 
plates  and  the  current. 

The  fall  of  potential  between  the  plates  is  made  up  of  the  fall 
of  potential  at  the  layers  which  we  have  already  calculated  and 
the  fall  of  potential  in  the  space  between  the  layers  where  the 
electric  intensity  is  uniform  and  equal  to  X0;  the  breadth  of  this 
space  is  I  —  (Xj  +  X2)  where  I  is  the  distance  between  the  plates, 
and  since  Xj  +  X2  is  equal  to  i/qe  the  fall  of  potential  in  this  space 
is  equal  to 

• 


adding  to  this  the  values  for  the  fall  of  potentials  across  the  layers 
we  get,  if  V  is  the  potential  difference  between  the  plates, 


38]  ELECTRICITY   THROUGH   A  GAS   CONTAINING   IONS.  73 


This  equation  is  of  the  form 

V=Ai*  +  Bi, 

thus  the  curve  whose  ordinate  is  i  and  abscissa  V  is  a  parabola. 
This  equation  ceases  to  be  an  approximation  to  the  truth  when 
the  two  layers  touch,  i.e.  when  \  +  \2  =  l  or  i  =  qel\  in  this  case 
the  current  is  the  greatest  that  can  be  carried  by  the  ionised  gas. 
The  minimum  value  of  the  potential  difference  required  to  pro- 
duce this  current  is  got  by  putting  i  =  qel  in  equation  (15);  we  see 
that  the  potential  difference  required  to  produce  saturation  is 
proportional  to  the  square  of  the  distance  between  the  plates  and 
to  the  square  root  of  the  intensity  of  ionisation. 

38.  The  study  of  the  distribution  of  electric  intensity  between 
the  plates  when  the  maximum  current  is  passing  leads  to  an  easy 
way  of  finding  the  ratio  of  the  velocities  of  the  positive  and  nega- 
tive ions,  for  as  in  this  case  there  is  no  recombination,  equations 
(5)  and  (6),  p.  65,  give 

RlnlX  =  qx  ..............................  (16), 

Rzn,X  =  q(l-x)    .....................  (17), 

where  x  is  measured  from  the  positive  plate.  At  the  point 
between  the  plates  where  the  force  is  a  minimum 


..         _         .       f  -. 

-—  =  0  =  4?r  (ft!  -  nz)  e, 

hence  at  this  point  7^  =  <rc2  ,  so  that  if  x  is  the  distance  of  the  po:nt 
P  where  X  is  a  minimum  from  the  positive  plate  we  have  by 
equations  (16)  and  (17) 


Ms     I  -a' 

thus  the  ratio  of  the  velocities  of  the  positive  and  negative  ions  is 
equal  to  the  ratio  of  the  distances  of  P  from  the  positive  and 
negative  plates,  so  that  if  we  have  determined  P  by  measuring 


74      MATHEMATICAL  THEORY  OF  THE  CONDUCTION  OF     [39 

the  distribution  of  potential  between  the  plates  we  can  at  once 
deduce  the  ratio  of  the  velocities. 

39.     Case  when  the  ionisation  is  confined  to  a  thin  layer. 

In  the  preceding  investigation  we  have  supposed  that  the 
ionisation  is  uniformly  distributed  between  the  plates,  there  are 
however  many  very  important  cases  when  the  region  in  which  the 
ionisation  takes  place  is  a  thin  layer  of  gas,  the  rest  of  the  space 
between  the  plates  being  free  from  the  action  of  the  ionising 
agent.  We  proceed  now  to  the  consideration  of  this  case,  begin- 
ning with  the  one  where  the  ionised  layer  is  close  to  one  of 
the  plates  A.  Let  us  suppose  that  A  is  the  positive  plate,  then 
all  the  ions  in  the  space  between  the  plates  must  have  been 
dragged  by  the  action  of  the  electric  field  from  the  layer,  hence 
these  ions  must  be  all  positive,  so  that  the  current  is  carried 
entirely  by  positive  ions.  Let  there  be  nx  of  these  ions  per 
cubic  centimetre  and  let  X  be  the  electric  force,  i  the  current, 
then  using  the  same  notation  as  before  our  equations  are  now 

dX 

^— 

dx 


from  these  equations  we  get 

XdX 

dx 

Z«  =          +  C...  ...(18), 

^i 

where  C  is  the  constant  of  integration;  it  is  evidently  the  value  of 
Xz  close  to  the  positive  plate. 

If  V  is  the  potential  difference  between  the  plates,  and  I  their 
distance  apart,  we  have 


To  find  an  expression  for  C  we  must  turn  our  attention  to  the 
layer  of  ionised  gas  ;  let  us  suppose  that  the  current  is  small  com- 
pared with  that  required  to  saturate  this  layer,  then  the  number 
of  free  positive  or  negative  ions  in  unit  volume  of  the  layer 
=  (qloty,  if  q  as  before  measures  the  intensity  of  ionisation  ;  if 


39]  ELECTRICITY  THROUGH  A  GAS  CONTAINING   IONS.  75 

there  is  no  great  change  in  the  electric  force  as  we  pass  from  the 
gas  into  the  layer  the  sum  of  the  velocities  of  the  positive  and 
negative  ions  will  be  of  the  order  (Rl  +  R2)  C*  and  as  i  the  current 
equals  the  number  of  ions  multiplied  by  the  sum  of  the  velocities 
of  the  ions,  e  (Rj.  +  jR2)  C*  (q/a)*  will  be  of  the  same  order  as  i ; 
hence  C  is  comparable  with 


Hence  C  will  be  small  compared  with  8iril/Rl  if 


is  a  small  quantity. 

If  8  is  the  thickness  of   the  ionised   layer,  /  the  saturation 
current, 

I  =  qe8; 

thus  the  preceding  quantity  will  be  small  if 

1  i  8       R9        1   . 

-  is  small, 

>2 


where  A  „  (ft  + 


OL 


If  8/1,  i/I  are  small,  then  since  /32  is  greater  and  R2/(Rl  4-  R%) 
less  than  unity,  we  see  that  the  quantity  under  consideration  will 
be  small.  When  this  is  the  case  we  can,  in  equation  (19),  neglect 

C  in  comparison  with  -^—  ,  and  the  equation  becomes 


We  see  that  in  this  case  the  current  is  proportional  to  the 
square  of  the  potential  difference,  and  thus  increases  more  rapidly 
with  the  electromotive  force  than  if  it  obeyed  Ohm's  law.  We 
shall  see  examples  of  this  when  we  consider  the  passage  of 
electricity  through  metals  immersed  in  hot  gases.  In  this  case  by 
far  the  greater  part  of  the  ionisation  occurs  in  the  layer  next  the 
metal  and,  as  Pringsheim*  has  shown,  the  current  increases  more 
rapidly  than  the  potential  difference.  The  current  is  proportional 
to  Rl  the  velocity  of  the  ion  which  carries  it;  thus  since  the 

*  Pringsheim,  Wied.  Ann.  55,  p.  507,  1895. 


76      MATHEMATICAL  THEORY  OF  THE  CONDUCTION  OF     [39 

velocity  of  the  negative  ion  is  greater  than  that  of  the  positive, 
the  current  for  the  same  difference  of  potential  between  the  plates 
is  greater  when  the  ionisation  takes  place  next  the  negative  plate 
than  when  next  the  positive,  in  other  words  the  current  is  greater 
in  one  direction  than  in  the  opposite;  this  unipolar  conductivity 
as  it  is  called  is  very  marked  indeed  in  conduction  through  hot 
gases  and  flames  containing  salts.  Rutherford*  has  observed  it 
when  the  ionisation  was  due  to  Rontgen  or  radium  radiation.  We 
see  from  (20)  that  for  a  given  potential  difference  the  current 
is  independent  of  q,  the  intensity  of  ionisation  ;  the  maximum 
currents  between  the  plates  will  of  course  depend  upon  the 
intensity  of  the  ionisation,  but  as  long  as  the  currents  are  only  a 
small  fraction  of  the  maximum  corresponding  to  the  smallest 
ionisation,  the  currents  will  be  independent  of  the  amount  of 
ionisation  next  the  plate  ;  we  see  too  that  the  current  does  not 
depend  on  the  charge  carried  by  the  ion. 

The  current  for  a  given  difference  of  potential  varies  inversely 
as  the  cube  of  the  distance  between  the  plates  ;  as  the  current 
varies  as  the  square  of  the  potential  difference,  if  we  keep  the 
average  electric  intensity  between  the  plates  constant  as  the 
distance  diminishes  the  current  will  vary  inversely  as  the  distance 
between  the  plates. 

When  the  ionisation  is  confined  to  a  layer  next  the  plate  A,  we 
can  stop  the  flow  of  ions  and  therefore  of  electricity  to  the  plate  B 
by  interposing  between  the  plates  a  third  plate,  and  the  passage 
of  electricity  will  be  stopped  just  as  effectually  by  a  plate  of 
metal  as  by  a  non-conductor  ;  thus  we  get  the  somewhat  para- 
doxical effect  of  completely  stopping  a  current  between  two 
plates  by  interposing  between  them  an  excellent  conductor  of 
electricity.  An  example  of  this  effect  will  be  considered  when 
we  discuss  the  passage  of  electricity  through  very  hot  gases. 

If  the  layer  of  ionised  gas  is  situated  between  the  plates  at  a 
distance  ^  from  the  positive  and  /2  from  the  negative  plate,  then 
if  V  is  the  potential  difference  between  the  plates,  we  can  easily 
prove  by  the  same  method  as  we  have  used  when  the  layer  was 
next  the  plate  that 


*  Eutherford,  Phil.  Mag.  vi.  2,  p.  210,  1901. 


39]  ELECTRICITY  THROUGH   A   GAS  CONTAINING   IONS.  77 

where  R^  and  E2  are  respectively  the  velocities  of  the  positive  and 
negative  ions.  We  see  that  if  ^  is  not  equal  to  E2  the  current 
for  the  same  potential  difference  will  not,  unless  Zx  =  l.2)  be  the 
same  in  one  direction  as  in  the  opposite.  If  the  velocity  of  the 
negative  ion  is  greater  than  that  of  the  positive,  the  current 
will  be  greatest  when  its  direction  is  such  that  the  negative  plate 
is  nearer  to  the  ionised  layer  than  the  positive.  From  this  we 
conclude  that  want  of  symmetry  in  the  distribution  of  ionisation 
will  give  rise  to  unipolar  conductivity.  The  distribution  of  electric 
intensity  when  the  ionised  layer  is  between  the  plates  is  repre- 
sented in  Fig.  25. 


The  preceding  results  are  only  true  when  the  electric  intensity 
close  to  the  ionised  layer  is  small  compared  with  its  value  some 
distance  away,  a  result  which  we  have  shown  will  be  the  case 
when  the  current  is  not  approaching  saturation,  provided  there  is 
not  a  great  increase  in  the  value  of  the  electric  intensity  as  we 
pass  from  the  inside  of  the  layer  to  a  point  just  outside.  There  are 
cases,  of  which  the  best  known  is  that  of  ultra-violet  light  falling 
on  a  metal  plate,  where  this  condition  is  not  fulfilled.  If  the 
illuminated  plate  is  made  the  negative  one,  a  current  of  electricity 
will  pass  from  it  to  a  neighbouring  plate,  but  in  this  case  the 
electric  field  between  the  plates  will  be  approximately  unifo.m 
and  the  preceding  results  do  not  apply.  We  may  explain  this  as 
follows:  we  shall  see  that  a  metal  plate  exposed  to  ultra-violet 
light  emits  negative  ions,  and  these  ions  like  cathode  rays  ionise 
the  gas  through  which  they  pass.  Consider  an  insulated  piece  of 
metal  in  air,  it  cannot  go  on  indefinitely  losing  negative  electricity, 
for  observation  proves  that  its  potential  does  not  go  on  increasing 
indefinitely ;  it  must  reach  a  stage  in  which  it  receives  as  much 


78  MATHEMATICAL  THEORY   OF   THE   CONDUCTION,   ETC.          [39 

negative  electricity  from  the  air  as  it  loses  by  the  action  of  the  light. 
We  can  see  how  this  can  be  brought  about :  suppose  A  is  the  surface 
of  the  metal,  next  this  we  have  a  layer  of  ionised  gas;  the  metal  loses 
negative  electricity  and  gets  a  positive  charge,  while  the  negative 
electricity  accumulates  and  forms  a  layer  at  some  little  distance  from 
the  plate.  The  layers  of  positive  and  negative  electricity  produce 


A 

Fig.  26. 

an  electric  field  which  tends  to  drive  the  negative  ions  in  the  ion- 
ised gas  between  them  into  the  metal,  the  stronger  this  field  the 
more  negative  ions  go  to  the  metal ;  the  electrification  in  the  layers 
will  accumulate  until  the  strength  of  the  field  is  such  that  as 
many  negative  ions  are  driven  by  it  from  the  gas  into  the  metal 
as  the  metal  loses  by  the  action  of  the  light.  In  passing  however 
from  the  inside  to  the  outside  of  the  layer  of  ionised  gas  we  have 
to  pass  across  a  layer  of  electricity,  this  will  produce  a  discon- 
tinuity in  the  electric  intensity  equal  to  4>7rcr,  where  cr  is  the 
surface  density  of  the  electrification ;  there  may  thus  be  a  great 
difference  between  the  electric  intensity  inside  the  layer  and  that 
just  outside,  so  that  the  reasoning  which  we  used  to  prove  X0  in 
equation  (19)  small  compared  with  87ril/R  need  not  apply  in 
this  case. 


CHAPTER  IV. 

EFFECT   PKODUCED   BY  A  MAGNETIC   FIELD   ON  THE 
MOTION   OF  THE   IONS. 

40.  WHEN  a  charged  ion  is  moving  in  a  magnetic  field  it 
experiences  a  mechanical  force  whose  direction  is  at  right  angles 
to  the  direction  of  motion  of  the  ion,  at  right  angles  also  to  the 
magnetic  force  and  equal  in  magnitude  to  HeVsmB,  where  H  is 
the  magnetic  force,  V  the  velocity  of  the  ion,  e  its  charge,  and  6 
the  angle  between  H  and  V\  H  and  e  are  to  be  expressed  in  the 
electromagnetic  system  of  units.  The  relation  between  the  direction 
of  this  force  F,  V  and  H,  for  a  positively  charged  ion,  is  shown  in 
Fig.  27. 


Fig.  27. 

Now  suppose  that  we  have  an  ion  moving  through  a  gas,  the 
viscosity  of  the  gas  causing  the  velocity  of  the  ion  to  be  propc  - 
tional  to  the  force  acting  upon  it.  Then  if  X,  Y,  Z,  are  the 
components  of  the  electric  intensity,  a,  /3,  7  those  of  the  magnetic 
force,  u,  v,  w  those  of  the  velocity,  the  mechanical  force  exerted  on 
the  ion  by  the  magnetic  field  has  for  components 

e  (ftw  —  rfo),     e  (yu  —  aw),     e  (av  —  /3u), 
while  the  components  of  the  mechanical  force  due  to  the  electric 


80  EFFECT   PRODUCED   BY  A  MAGNETIC   FIELD  [40 

field  are  Xe,  Ye,  Ze.     Thus  as  the  velocity  of  the  ion  is  proportional 
to  the  mechanical  force  acting  upon  it  we  have 

u  =  R  (X  +  fiw  -  ryv)\ 

v  =  R(Y+ryu-aw)[ (1), 

w  =  R  (Z  +  OLV  -  fin)) 

R  is  evidently  the  velocity  of  the  ion  under  unit  electric  intensity 
when  there  is  no  magnetic  field.     Solving  equations  (1)  we  find 

RX  +  R*  (yY-/3Z)  +  R*a(aX  +  /3F+  yZ) 


u  = 


(a2  +  £2  +  72) 


=  \ 

22        2       2  ' 


R*({3X-aY)  +  R*y  (aX  +  j3Y  +  yZ) 


= 


The  first  term  in  the  numerator  of  these  expressions  represents 
a  velocity  parallel  and  proportional  to  the  electric  force  ;  the 
second  term  a  velocity  at  right  angles  both  to  the  electric  and 
magnetic  forces  and  proportional  to  R2HFsm  (f>  ;  where  H,  F,  and 
<£  represent  respectively  the  magnetic  and  electric  forces  and  the 
angle  between  them  ;  the  third  term  represents  a  velocity  parallel 
to  the  m'agnetic  force  and  proportional  to  RsH2Fcos  (/>.  The 
relative  importance  of  these  terms  depends  upon  the  value  of  RH, 
if  this  quantity  is  small  the  first  term  is  the  most  important  and 
the  ion  moves  parallel  to  the  electric  force,  if  on  the  other  hand 
RH  is  large  the  last  term  is  the  most  important  and  the  ion 
moves  parallel  to  the  magnetic  force.  Since  R  is  the  velocity  of 
the  ion  under  unit  electric  force,  and  the  unit  force  on  the  electro- 
magnetic system  is  10~8  of  a  volt  per  cm.,  the  value  of  R  for  an  ion 
moving  through  air  at  atmospheric  pressure  would  be  1*5  x  10~8, 
since  the  velocity  of  the  ion  under  a  volt  per  cm.  is  about 
I'D  cm./sec.  Thus  at  atmospheric  pressure  it  would  not  be  feasible 
to  get  a  magnetic  field  strong  enough  to  make  RH  large.  As  R 
varies  inversely  as  the  pressure  of  a  gas  through  a  considerable 
range  of  pressures  it  might  at  very  low  pressures  be  possible 
to  make  RH  large  and  thus  make  the  ions  travel  along  the  lines 
of  magnetic  force. 

Let  us  take  the  case  of  an  ion  placed  in  a  field  in  which  both 
the  electric  and  magnetic  forces  are  uniform  ;  let  the  electric  force 


41]  ON  THE  MOTION   OF  THE   IONS.  81 

be  parallel  to  the  axis  of  x  and  let  the  magnetic  force  be  in  the 
plane  of  xzt  then  Y=  0,  Z  =  0,  /3  =  0,  and  equations  (2)  become 

U  =  1  +  R2  (a2  +  72)  =  RX  aPProximately>  if-  &  («2  +  72)  is  small, 


Thus  the  effect  of  the  magnetic  force  is  to  give  the  ion  a 
velocity  -  Ryu,  at  right  angles  to  both  the  electric  and  magnetic 
forces  and  a  velocity  R*y  (a2  +  72)*  w  in  the  plane  of  xz  at  right 
angles  to  the  magnetic  force. 

If  both  positive  and  negative  ions  are  present  and  if  Rl  is  the 
value  of  R  for  the  positive  and  R2  that  for  the  negative  ion,  and  if 
u1}  vl}  w^  u2,  v2,  w2  are  respectively  the  velocities  of  the  positive 
and  negative  ions,  then  if  there  are  n  positive  and  negative 
ions  per  unit  volume  the  current  parallel  to  y  will  be  equal  to 
ne  fa  —  v2)  or,  substituting  the  values  of  ^  and  v2,  to 


if  I  is  the  main  current  parallel  to  x  ;  thus  if  the  velocities  of  the 
positive  and  negative  currents  are  unequal  the  magnetic  field  will 
give  rise  to  a  side  current  proportional  to  the  main  one  and  the 
direction  of  the  current  will  be  deflected  through  an  angle  whose 
tangent  is  (R2  —  RJ  y.  If  we  retain  terms  proportional  to  (Rff)2, 
where  H  is  the  magnetic  force,  we  see  that  there  will  be  an 
additional  current  proportional  to  (Rf  +  R22  —  RA)  y  (a2  +  72)*  / 
in  the  plane  of  xz  at  right  angles  to  the  magnetic  force. 

When  the  electric  field  is  not  uniform  but,  like  that  due  to 
a  charged  particle,  radiates  from  a  point  we  can  prove  without 
difficulty  that  an  ion  in  a  uniform  magnetic  field  will  describe 
a  spiral  traced  on  a  cone  of  revolution,  the  axis  of  the  cone  being 
parallel  to  the  magnetic  force. 

Motion  of  a  free  ion  in  a  magnetic  field. 

41.   If  the  ion  instead  of  having  to  move  through  the  molecules 

of  a  gas  is  moving  in  a  vacuum,  the  path  it  describes  in  a  uniform 

magnetic  field  is  readily  found.     We  shall  first  of  all  take  the  case 

when  no  electric  forces  act  upon  the  ion,  then,  since  the  only  force 

T.  G.  6 


82  EFFECT   PRODUCED   BY   A   MAGNETIC   FIELD  [42 

acting  on  the  ion  is  that  due  to  the  magnetic  field  and  this  force 
is  always  at  right  angles  to  the  path  of  the  ion,  the  velocity  of  the 
ion  will  be  constant  ;  again  since  the  force  is  at  right  angles  to 
the  magnetic  force,  there  will  be  no  acceleration  parallel  to  this 
force,  thus  when  the  magnetic  field  is  uniform  the  component 
of  the  velocity  parallel  to  the  magnetic  force  is  constant.  As 
the  resultant  velocity  is  constant  this  implies  that  the  direction 
of  motion  of  the  ion  makes  a  constant  angle  with  the  magnetic 
force.  If  p  is  the  radius  of  curvature  of  the  path  of  the  ion,  m  its 

'777??^ 

mass,  v  its  velocity,  the  force  along  the  normal  is  equal  to  —  ,  but 

this  force  is  equal  to  Hev  sin  0,  where  H  is  the  magnetic  force  and 
0  the  angle  between  v  and  H,  e  the  charge  on  the  ion,  thus 


TT        -     a 

-  =  lievsin  u, 
P 


mv 


Thus  as  v  and  0  are  constant  the  radius  of  curvature  of  the  path 
is  constant,  the  path  of  the  particle  is  therefore  a  helix  wound  on 
a  circular  cylinder  whose  axis  is  parallel  to  the  lines  of  magnetic 
force,  the  radius  of  the  cylinder  is  p  sin2  6  or  mv  sin  OjeH*.  If  the 
particle  is  projected  at  right  angles  to  the  lines  of  magnetic  force, 
the  helix  shrinks  into  a  circle  whose  radius  is  mv/eH:  as  the  path 
in  this  case  is  a  closed  one  the  ion  never  travels  more  than  a  finite 
distance  from  its  point  of  projection.  If  the  velocity  of  the  ion  has 
a  component  parallel  to  the  magnetic  force,  this  component  remains 
constant  and  the  ion  goes  on  describing  equal  spaces  parallel  to 
the  magnetic  force  in  equal  times,  while  in  a  direction  at  right 
angles  to  the  magnetic  force  the  velocity  of  the  ion  is  sometimes 
in  one  direction  and  sometimes  in  the  opposite,  so  that  the  ion, 
however  long  it  moves,  never  travels  more  than  a  finite  distance 
from  the  line  of  force.  We  may  thus  express  the  general  features 
of  the  effect  by  saying  that  in  the  magnetic  field  the  ions  tend 
to  follow  the  lines  of  magnetic  force. 

42.  The  preceding  investigation  relates  to  the  case  when  the 
magnetic  field  is  constant  and  the  lines  of  magnetic  force  do  not 
change  their  direction;  it  is  of  interest  to  see  whether  the  ions  will 

*  G.  G.  Stokes,  Proc.  Roy.  Soc.  Mar.  30,  1876  ;  Phil.  Mag.  v.  2,  p.  359,  1876. 


42]  .  ON   THE   MOTION   OF  THE  IONS.  83 

continue  to  follow  the  lines  of  magnetic  force  when  these  change 
their  direction  from  point  to  point.  We  shall  take  the  special  case 
when  the  lines  of  magnetic  force  are  circles  round  the  axis  of  z,  the 
field  being  that  due  to  a  current  i  flowing  along  this  axis  ;  in  this 
case  if  a,  (3,  7  are  the  components  of  magnetic  force  at  a  point 
whose  coordinates  are  #,  y,  z, 

2iy  2ix 

«  =  >     0=-'     7=°' 


and  if  m  is  the  mass  of  the  ion,  e  its  electric  charge,  we  have 
d?x  2ix\  dz 


d2y 


From  these  equations  we  have 

6HS)'+ ®- 

where  Fis  the  velocity  of  projection  of  the  ion; 


Thus  if  p  and  0  are  the  polar  coordinates  in  the  plane  xy,  of 
the  ion, 


where  h  is  a  constant ; 

dz  2ei  i  ,  n 
—  =  -  log  p  +  Ct 
dt  m 

where  C  is  a  constant:  thus  the  orbit  of  the  ion  in  the  plane  of 
xy  is  that  of  a  particle  of  mass  m  acted  on  by  a  central  attractive 

force  equal  to  (-  -  log  p  +  2ei  G\  jp. 
Since 


we  have  .  , 

v^y        p"2  Vm  e_2 


84  EFFECT  PRODUCED   BY    A  MAGNETIC   FIELD  [43 

Since  f  -j.  j   is  essentially  positive,  p  will  always  lie  between  the 
greatest  and  least  roots  of  the  equation 


so  that  the  ion  will  always  remain  at  a  finite  distance  from  the 
axis  of  z. 

43.  Let  us  consider  some  special  cases.  Let  the  ion  be  pro- 
jected parallel  to  the  lines  of  magnetic  force  from  the  point  p  =  a  : 
then  since  dz/dt  =  0  when  p  =  a,v?e  have 

dz  _  Zei  ,      p 
dt~  m    °%  a  ' 

and  h  =  Fa, 

fdp\2      T7.9  /.,      a2\      f2ei ,      p\2 
hence  -£     =  F2  ( 1 —  log  "     ; 

\dtJ  \        p2J      \m     6a/  ' 

from  this  equation  we  see  that  p  can  never  be  less  than  a,  and  thus 
the  velocity  parallel  to  the  axis  of  z  never  changes  sign :  again  p 
never  exceeds  the  value  R}  given  by  the  equation 

2ei       R_, 
JYI         a 

R  =  a  satisfies  this  equation  but  there  is  another  root  greater 
than  a ;  it  is  this  root  which  is  the  maximum  value  of  p. 

Thus  in  the  plane  at  right  angles  to  the  axis  of  z  the  ion 
circulates  in  an  orbit  included  between  the  circles  p  =  a  and  p=R'y 
and  thus  again  the  ion  moves  in  the  general  direction  of  the  lines 
of  magnetic  force,  although  in  this  case  there  is  a  drift  of  the  ions 
parallel  to  the  axis  of  symmetry  of  the  magnetic  field.  If  F  is 
small  compared  with  2ei/mt  the  solution  of  the  equation  (1)  is 


In  this  case  the  maximum  velocity  parallel  to  z  is  V.(V/eim) 
and  is  thus  small  compared  with  F.  Thus  the  smaller  the 
velocity  of  projection  and  the  stronger  the  field  the  more  nearly 
does  the  path  of  the  ion  coincide  with  a  line  of  magnetic  force. 


45]  ON   THE   MOTION   OF  THE   IONS.  85 

44.  In  the  next  case  the  ion  is  projected  from  p  =  a  in 
a  direction  parallel  to  z,  in  this  case  h  =  0  and  the  path  of  the 
ion  is  in  the  plane  through  the  axis  of  z  and  the  point  of  pro- 
jection; if  V  is  the  velocity  of  projection,  then 

dz  2ei  ,  p  Tr 
—  =  —  log  £  +  Y: 
dt  m  6  a 

now  dz/dt  can  never  be  greater  numerically  than  V,  hence  if  V 
and  2ei/m  are  of  the  same  sign  p  can  never  be  greater  than  a. 

The  values  between  which  p  oscillates  are  a  and  ae  eilm  ;  the 
orbit  is  a  closed  one  and  its  dimensions  are  very  small  if  V  is  small 
compared  with  ei/m.  If  Y  and  ei/m  are  of  opposite  signs  then  we 
can  show  that  p  is  never  less  than  a  and  varies  between  a  and 


45.  A  third  case  we  shall  consider  is  when  the  particle  is  pro- 
jected with  velocity  V  parallel  to  p  from  p  =  a,  in  this  case  again 
h  =  Q,  but 

dz     2ei ,      p 

—  =  —  log  -  . 
dt      m     °  a 

Since  dz/dt  can  never  be  greater  numerically  than  V  we  see 

mV  mV 

that  p  must  lie  between  the  limits  p  =  ae2ei  and  p  =  ae  2et;  the 
orbit  is  in  the  plane  through  the  axis  of  z  and  the  point  of 
projection.  If  the  magnetic  field  is  very  strong  and  therefore 
mV/Zei  small,  p  is  always  very  nearly  equal  to  a,  let  it  equal 
a  (1  -f  f),  our  equations  are  then  approximately 

d*%  _  _/2ef\2jr 
di?  ~  ~  \m)  a?  ' 

dz  _  2ei  £ 
dt       m 
the  solution  of  which  is 


2t  e 

z  =  aA  cos  —  —  t. 
a  m 

Since  V=  a  ^  when  *=  0,  aA  =  V™  j.=  ^   when   H   is   the 
magnetic  force  at  the   point  of  projection.     Thus,  as  we  might 


86  EFFECT  PRODUCED   BY  A   MAGNETIC   FIELD  [46 

have  expected,  the  path  in  this  case  is  a  circle  whose  radius  aA  is 
equal  to  (F/J7)(m/e). 

We  see  from  the  consideration  of  the  variable  field  as  well  as 
from  that  of  the  constant  one  that  the  ion  will  tend  to  follow  the 
lines  of  magnetic  force,  except  in  the  very  special  case  when  the 
circumstances  of  projection  are  such  that  the  ion  during  its  motion 
always  cuts  the  lines  of  magnetic  force  at  right  angles. 

Motion  of  an  ion  under  the  joint  action  of  electric  and 
magnetic  forces. 

46.  We  shall  now  investigate  the  motion  of  an  ion  when  it 
is  acted  on  simultaneously  by  both  electric  and  magnetic  forces; 
we  shall  take  the  case  when  both  these  forces  are  constant.  Let 
the  axis  of  z  be  parallel  to  the  direction  of  the  magnetic  force, 
and  the  plane  of  xz  parallel  to  the  direction  of  the  electric  force. 
Let  H  be  the  magnetic  force,  X,  0,  Z  the  components  of  the 
electric  force,  then  if  m  is  the  mass  of  an  ion,  e  its  charge,  and 
x,  y,  z  its  coordinates  the  equations  of  motion  are 


From  equation  (3)  we  have 

•  -JJl'-fiM  ........................  (4), 

where  w0  is  the  velocity  of  projection  parallel  to  z,  the  origin  of 
coordinates  being  supposed  to  be  taken  at  the  point  of  projection. 

From  equations  (1)  and  (2)  we  have 
j^ 

y-c+  fTt  +  Acoscot  +  B  sin  cot    ............  (5), 

Jj.  , 

x  —  a  —  A  sin  cot  +  B  cos  cot  .....................  (6), 

where   a,   c,  A  and    B  are   arbitrary   constants   and   a)  =  He/m. 
Writing  equations  (5)  and  (6)  in  the  form 

V 

y  —  c  =  —  ,j.  cot  +  A'  cos  (cot  —  a), 

CO  £1 

x  —  a  =  —  A'  sin  (cot  —  a)  ; 


46]  ON    THE   MOTION    OF   THE   IONS.  87 

we  see  that  the  projection  of  the  path  of  the  ion  on  the  plane 
of  xy  is  a  trochoid,  generated  by  a  circle  whose  radius  is  X/coH 
rolling  on  a  line  perpendicular  to  the  electric  force,  the  distance 
of  the  tracing  point  from  the  centre  of  the  rolling  circle  being  A'. 
Since  the  average  value  of  the  periodic  terms  tends  to  vanish 
when  the  time  over  which  the  average  extends  is  large  compared 
with  l/o)  we  see,  from  equations  (5)  and  (6),  that  the  equations 


x  =  a, 

give  the  average  positions  of  the  ion,  and  that  the  average 
velocity  parallel  to  y  is  X/H  while  that  parallel  to  x  vanishes. 

As  the  velocity  parallel  to  z  at  the  time  t  is  —  t  +  w0  we  see  that 

m 

if  Z  is  finite  the  velocity  parallel  to  z  will  ultimately  become 
infinite  compared  with  the  components  parallel  to  the  other 
axes,  thus  in  this  case  the  ions  will  ultimately  move  along  the 
lines  of  magnetic  force  ;  we  must  remember  however  that  this 
reasoning  only  applies  when  the  electric  field  has  a  finite  com- 
ponent in  this  direction. 

If  we  determine  the  constants  in  (5)  and  (6)  in  terms  of  v0,  u0, 
the  initial  values  of  the  components  of  the  velocity  of  projection 
of  the  ion  parallel  to  the  axes  of  y  and  x  respectively,  we  have, 
the  origin  being  taken  at  the  point  of  projection, 

y  =  —  °(1  -coscot)  +  Tft  +  [vo-^J-sin  wt  .........  (7), 

co  H         \        rLJ  co 

CJ\.  \   \.     ,  ~  j\     .     ^0      •  ±  /O\ 

rr  —  fy  1  —  (1  —  COS       '  +  —  Sin  0>£     ...............  (o). 
n.         )  co  co 

If  JT=0,  i.e.  if  the  directions  of  the  electric  and  magnetic 
forces  coincide,  we  have 


thus  the  projection  of  the  path  of  the  ion  on  the  plane  of  xy  is 
a  circle  and  the  path  of  the  ion  is  a  helix  of  gradually  increasing 
pitch  with  its  axis  parallel  to  the  lines  of  magnetic  force. 


88  EFFECT  PRODUCED   BY  A   MAGNETIC    FIELD  [47 

If  Z  =  0,  i.e.  if  the   electric  force  is  at  right   angles  to  the 
magnetic,  and  if  in  addition  u0,  VQ,  WQ  all  vanish,  we  have 

TT 

y  —  —f  (tot  —  sin  wt), 


•v 

X  —  —  rr  (1  —  COS  0)t). 

wii 

This  is  the  equation  to  a  cycloid,  the  radius  of  the  generating 
circle  being  XjwH  or  Xm/eH2,  the  line  on  which  it  rolls  is 
perpendicular  to  the  electric  force.  The  greatest  distance  which 
the  particle  can  get  from  its  point  of  projection  measured  in  the 
direction  of  the  electric  force  is  2Xm/eH2,  the  average  velocity 
in  this  direction  is  zero  while  the  average  velocity  parallel  to  y, 
i.e.  in  the  direction  at  right  angles  both  to  the  electric  and 
magnetic  forces,  is  finite  and  equal  to  X/H.  If  the  ion  were 
projected  with  the  velocity  w  parallel  to  the  axis  of  z  it  would 
retain  this  velocity  unaltered  and  the  average  direction  of  motion 
of  the  ion  would  be  at  right  angles  to  the  electric  force  and  along 
a  line  making  an  angle  i^rrlXjwH  with  the  direction  of  the 
magnetic  force. 

47.     If  w0  =  0  and  v0  =  X/H  we  have 

y  =  v<>t, 


Thus  in  this  case  the  path  of  the  ion  in  the  plane  of  xy  is  the 
same  as  if  there  were  neither  electric  nor  magnetic  forces  acting 
upon  it :  the  force  Xe  acting  on  the  particle  due  to  the  electric 
field  is  in  this  case  just  balanced  by  the  force  Hev  due  to  the 
magnetic  field. 

48.  Returning  to  the  general  case  represented  by  equations 
(7)  and  (8)  we  easily  deduce  that  the  maximum  velocity  F  parallel 
to  the  plane  of  xy  attained  by  the  ion  is  given  by  the  equation 

F  *+wf-«.)T- 

H     (         \H         )} 

thus  until  u0  and  VQ  are  comparable  with  X/H,  the  maximum 
velocity  attained  is  very  approximately  ZX/H  and  is  independent 
of  the  velocity  of  projection,  and  the  charge  and  the  mass  of 
the  ion. 


49]  ON   THE   MOTION   OF  THE   IONS.  89 

The  maximum  displacement  f  measured  parallel  to  the  direc- 
tion of  the  electric  force  is  given  by  the  equation 


~V 


and  thus  until  u0  and  v0  become  comparable  with  X/H  the  distance 
travelled  by  the  ion  parallel  to  the  lines  of  electric  force  will  be 
very  approximately  independent  of  the  velocity  of  projection  of 
the  ion. 

It  will  be  gathered  from  the  preceding  discussion  that  except 
in  the  special  case  when  the  electric  and  magnetic  forces  are 
at  right  angles  to  each  other,  the  ions  ultimately  travel  along 
lines  of  magnetic  force. 

49.  The  case  when  the  electric  and  magnetic  forces  are  at 
right  angles  to  each  other  is  however  a  very  important  one  as  it 
includes  the  fields  produced  by  electric  waves.  In  these  waves 
the  electric  and  magnetic  forces  are  not  constant  but  in  the  case 
of  a  simple  harmonic  wave  may  be  taken  as  proportional  to  cospt. 
When  the  waves  are  all  divergent  the  electric  force  is  equal  to 
V  times  the  magnetic  force,  where  V  is  the  velocity  with  which 
the  electric  waves  travel  through  the  medium.  Thus  if  the 
direction  of  propagation  of  the  wave  is  parallel  to  the  axis  of  y 
and  if  the  magnetic  force  is  parallel  to  the  axis  of  z  and  equal  to 
#o  cos  0,  the  electric  force  will  be  parallel  to  the  axis  of  x  and 


equal  to  VBQ  cos  6  where  0  =  p(t-  ^j  .     The  equations  of  motion 
of  a  charged  particle  acted  on  by  this  electric  wave  are 


d?y       dx 


From  these  equations  we  have,  if  dx/dt  and  6  vanish  simul 

taneously, 

dx  e  V  „    .     - 


ra 


90  EFFECT  OF   MAGNETIC   FIELD   ON   MOTION   OF   IONS.          [49 

The  character  of  the  motion  of  the  ions  will  depend  upon  the  value 
of  H0e/pm ;  if  this  quantity  is  large  the  average  velocity  of  the 
ions  parallel  to  x  will  vanish  while  that  parallel  to  y  will  be  equal 
to  V:  thus  the  wave  will  in  this  case  carry  the  charged  particles 
along  with  it.  When  however  H0e/pm  is  a  small  quantity  the 
effect  of  the  wave  will  be  to  superpose  on  the  undisturbed  motion 
a  small  vibratory  motion  parallel  to  the  electric  force  in  the  wave 
and  thus  at  right  angles  to  its  direction  of  propagation. 


CHAPTER  V. 

DETEKMINATION  OF  THE  RATIO  OF  THE  CHARGE  TO 

THE  MASS  OF  AN  ION. 

50.  THE  value  of  e/m — the  charge  on  an  ion  divided  by  its 
mass — has  been  determined  by  the  application  of  some  of  the 
results  discussed  in  the  preceding  chapter.  The  first  case  we 
shall  consider  is  that  of  the  ions  in  the  cathode  rays. 

In  the  chapter  on  cathode  rays  we  shall  give  the  evidence 
which  leads  us  to  the  conclusion  that  the  cathode  rays,  i.e.  the 
streams  which  in  a  highly  exhausted  tube  through  which  an  electric 
discharge  is  passing  start  from  the  cathode  and  produce  a  vivid 
phosphorescence  when' they  strike  against  the  glass  of  the  tube, 
consist  of  negatively  electrified  particles  starting  from  the  neigh- 
bourhood of  the  cathode  and  moving  with  a  very  hign  velocity 
along  straight  lines.  Assuming  that  this  is  the  nature  of  the 
cathode  rays  we  shall  show  here  how  to  determine  the  velocity 
of  the  particles  and  the  value  of  e/m.  Suppose  that  we  have  a 
highly  exhausted  tube  of  the  pattern  shown  in  Fig.  28. 


Fig.  28. 

In  this  tube  C  is  the  cathode,  A  the  anode,  B  is  a  thick  metal 
disc  connected  with  the  earth,  holes  a  millimetre  or  so  in  diameter 
are  bored  through  the  middle  of  the  disc  and  through  the  anode ; 
some  tqf  the  cathode^  rays  starting  from  the  neighbourhood  of  the 


92  DETERMINATION   OF  THE  RATIO   OF  [50 

cathode  pass  through  these  holes,  thus  in  the  part  of  the  tube  to ' 
the  right  of  the  disc  we  have  a  pencil  of  negatively  electrified 
particles  travelling  along  straight  lines  parallel  to  the  line  joining 
the  holes  in  the  discs,  the  place  where  they  strike  the  glass  being 
marked  by  a  patch  of  bright  phosphorescence  p.  Suppose  now 
that  the  tube  is  placed  in  a  uniform  magnetic  field,  the  lines  of 
force  being  at  right  angles  to  the  path  of  the  ions,  the  paths  of  the 
ions  will  now  be  circles,  the  radii  of  the  circles  being  (see  p.  82) 
mv/eH,  where  m  is  the  mass  of  the  ion,  e  its  charge,  v  its  velocity, 
and  H  the  strength  of  the  magnetic  field.  The  place  at  which 
these  particles  strike  the  tube  will  no  longer  be  at  p  but  at  some 
other  point  p'y  the  direction  of  pp  being  at  right  angles  to  the 
magnetic  force.  Since  op'  is  an  arc  of  a  circle  of  which  op  is  a 
tangent,  we  have 

pp' (2R  +  pp')  =  op*, 
where  R  is  the  radius  of  the  circle  ;  hence 

:  '  **-$-*•  • 

or,  since  R  =  mv/eH,  we  have 

-  9  mv  _  op2         , 

If  the  magnetic  field  is  not  uniform  we  may  proceed  as  follows. 
Since  p  the  radius  of  curvature  at  any  point  of  the  path  of  the 
ion  is  given  by  the  equation 

p      vm' 

and  since,  when  the  path  of  the  ion  is  fairly  flat  l/p  is  very 
approximately  equal  to  dzyjdx2  where  y  and  x  are  the  coordinates 
of  the  ion,  x  being  measured  along  the  undisturbed  path,  and  y  at 
right  angles  to  it.  We  have 

ds?     vm ' 
so  that 

»:•;  ...(i). 


V 

Hence   if    we   measure  pp    and   know   the   distribution   of  the 
magnetic    force   H   along   the   tube    we  can  from  this  eolation 


50]  THE   CHARGE  TO   THE   MASS  OF  AN   ION.  93 

determine  the  value  of  e/vm.  This  gives  us  a  relation  between  v 
and  m/e.  We  can  determine  v  in  the  following  way  :  two  parallel 
metal  plates  D  and  E  are  placed  in  the  tube,  the  plates  being  parallel 
to  the  lines  of  magnetic  force  and  parallel  also  to  the  undisturbed 
path  of  the  rays  ;  these  plates  are  maintained  at  a  known  difference 
of  potential  by  connecting  them  to  the  terminals  of  a  battery.  Thus 
we  have  an  electric  field  between  the  plates  the  lines  of  force  of 
which  are  at  right  angles  to  the  lines  of  magnetic  force  and  to  the 
direction  of  motion  of  the  ions  ;  this  electrostatic  force  Y  tends  to 
deflect  the  ions,  the  force  acting  on  an  ion  being  Ye±  the  force  due 
to  the  magnetic  field  acts  in  the  same  straight  line  and  is  equal 
to  Hev.  Adjust  the  sign  of  the  difference  of  potential  so  that  the 
electric  and  magnetic  forces  tend  to  oppose  each  other,  then  keeping 
one  of  the  forces  fixed,  say  the  electric  force,  alter  the  value  of  the 
other  until  the  two  forces  just  balance,  this  stage  can  be  ascertained 
by  observing  when  the  phosphorescent  patch  p'  is  restored  to  its 
undisturbed  position.  When  this  stage  is  reached  we  have 

Ye  =  Hev, 

Y 
or  v  =  jj     ..............................  (2). 

Thus  by  measuring  Y/H  we  can  determine  the  velocity  of  tne 
ions  composing  the  cathode  rays.  As  we  know  e/vm  from  the 
experiments  on  the  magnetic  deflection  we  can  in  this  way  deduce 
the  values  of  both  e/m  and  v.  Equation  (2)  depends  upon  the 
assumption  that  both  the  magnetic  and  electric  fields  are  uniform, 
if  this  condition  is  not  fulfilled  we  must  proceed  as  follows. 
Suppose  that  p"  is  the  displaced  position  of  p  when  the  electric 
field  alone  is  acting  on  the  rays,  then  we  can  prove  without 
difficulty  that 


hence  if  we  know  the  distribution  of  the  electric  field  and  the 
value  of  pp"  we  can  by  equation  (3)  find  the  value  of  e/v*m  and 
since  by  equation  (2)  we  can  determine  e/vm  we  have  the  data 
for  determining  both  v  and,  e/m. 

In  order  to  apply  this  method  it  is  necessary  that  the  pressure 
of  the  gas  in  the  discharge  tube  in  which  the  rays  are  produced 
should  be  very  low;  the  passage  of  cathode  rays  through  a  gas 


94 


DETERMINATION    OF   THE   RATIO   OF 


[50 


makes  it  a  conductor  and  thus  as  the  rays  are  shielded  from  the 
electrostatic  field  by  the  gas  through  which  they  move  the  electro- 
static repulsion  is  hardly  appreciable  ;  if,  however,  the  pressure  of 
the  gas  is  very  low  the  conductivity  of  the  gas  is  so  small  that 
there  is  hardly  any  appreciable  shielding  effect  and  the  deflection 
produced  by  the  electric  field  is  easily  observed. 

Using  this  method  the  author  in  1897*  obtained  the  values  for 
v  and  e/m  given  in  the  following  table :  the  first  column  contains 
the  name  of  the  gas  filling  the  tube :  the  different  numbers  given 
under  one  gas  relate  to  experiments  made  at  different  pressures. 


Gas 

V 

mfe 

Gas 

V 

mje 

Air 

2-8  x  109 

1-3  xlO"7 

Air*     ... 

2-8  x  109 

1-1  x  10~7 

Air  

2'8  x  109 

1-1  x  10~7 

Hydrogen 

2-5  x  109- 

l-5xlO~7 

Air  

2-3  x  109 

l-2xlO~7 

Carbonic  ) 

Air* 

3*6  x  109 

l-3xlO~7 

acid       ( 

2'2x  109 

1'SxlO    r 

The  mean  of  the'values  of  m/e  is  1/3  x  10~7  or  e/m  =  77  x  106. 
We  see  too  that  within  the  limits  of  the  errors  of  the  experiments 
the  value  of  e/m  is  th«  same  whether  the  tube  be  filled  with  air, 
hydrogen  or  carbonic  acid,  so  that  it  does  not  depend  upon  the 
nature  of  the  gas.  This  result  was  first  obtained  by  the  writer  •(• 
by  another  method ;  the  pressure  in  the  discharge  tube  was 
adjusted  so  that  the  potential  difference  between  the  electrodes 
in  the  discharge  tube  was  the  same  for  all  the  gases  tried,  photo- 
graphs were  taken  of  the  rays  when  deflected  by  a  constant 
magnetic  field  and  from  these  it  was  found  that  the  deflected  rays 
occupied  the  same  position  whether  the  gas  in  the  tube  was 
hydrogen,  air,  carbonic  acid  or  methyl  iodide ;  these  gases  give  a 
wide  range  of  densities  as  the  density  of  methyl  iodide  is  about 
70  times  that  of  hydrogen.  The  constancy  of  the  value  of  e/m  for 
the  ions  which  constitute  the  cathode  rays  is  in  striking  contrast 
to  the  variability  of  the  corresponding  quantity  in  the  ions  which 
carry  the  current  through  liquid  electrolytes.  Experiments  were 
made  on  the  effect  of  altering  the  metal  of  which  the  cathode  was 
made,  the  experiments  marked  with  an  asterisk  in  the  preceding 


*  J.  J.  Thomson,  Phil  Mag.  v.  44,  p.  293,  1897. 

t  J.  J.  Thomson,  Proc.  Camb.  Phil  Soc.  ix.  p.  243,  1897. 


51] 


THE    CHARGE   TO   THE   MASS   OF   AN   ION. 


95 


table  were  made  with  platinum  electrodes,  all  the  others  were 
made  with  aluminium  electrodes ;  it  will  be  seen  that  the  values  of 
e/m  are  the  same  in  the  two  cases.  A  further  series  of  experiments 
on  this  point  has  been  made  by  H.  A.  Wilson*  who  used  cathodes 
made  of  aluminium,  copper,  iron,  lead,  platinum,  silver,  tin  and 
zinc  and  found  the  sanle  value  for  e/m  in  all  cases. 

If  we  compare  tjle  value  of  e/m  viz.  77  x  106  for  the  ions  in  the 
cathode  rays  with/the  value  of  the  corresponding  quantity  for  the 
ions*  which  carry  the  current  through  liquid  electrolytes  we  are 
led  to  some  very  interesting  conclusions ;  the  greatest  value  of  e/m 
in  the  case  of  liquid  electrolysis  is  when  the  ion  is  the  hydrogen 
ion,  in  this  case! e/m  is  about  104.  When  we  discuss  the  electric 
charge  carried  w  the  ion  in  the  cathode  rays  we  shall  find  that 
it  is  equal  in  magnitude  to  the  charge  carried  by  the  hydrogen 
ion,  ki  liquid  electrolysis ;  it  follows  then  that  the  mass  of  the 
hydrogen  ion  mus^  be  770  times  that  of  the  ion  in  the  cathode 
rays  /hence  the  carrier  of  the  negative  electricity  in  these  rays 
must  be  very  small  compared  with  the  mass  of  the  hydrogen  atom. 
We  shall  return  to  this  point  when  we  have  studied  other  pheno- 
mena involving  gaseous  ions. 

0 1 
Ions  in  Lenard  rays. 


51,  Lenard  f  has  determined  by  the  method  just  described  the 
velocity  alodrthe  value  of  e/Tft  for  tne  Lenard  rays;  these  are  cathod 
rays  which  have  escaped  from  the  discharge  tube  through  a  window 
of  very  thin  aluminium  foil.  In  his  experiments  after  escaping 
from  the  discharge  tube  they  entered  a  highly  exhausted  vessel 
where  they  were  deflected  by  electric  and  .magnetic  fprces  in  the 
way  described  in  the  preceding  article ;  e  results  of  these 
experiments  are  given  in  the  following  tabl 


v  cm./sec. 

^4m 

67  x  109 

6-49  X  106 

7    xlO9 

6-32  x  10° 

8-1  x  109 

6-36  xlO6 

*  H.  A.  Wilson,  Proc.  Camb.  Phil.  Soc.  xi.  p.  179,  1901. 
f  Lenard,  Wied.  Ann.  xliv.  p.  279,  1898. 


96 


DETERMINATION    OF   THE    RATIO    OF 


[51 


The  mean  of  the  values  of  e/m  is  6'39  x  106  which  agrees  well 
with  the  value  7'7  x  106  found  above.  It  will  be  noticed  that  the 
velocities  of  the  ions  in  this  case  are  much  greater  than  in  the 
preceding,  taking  the  two  sets  together  we  have  velocities  of  the 
ions  ranging  from  2-2  x  10°  to  81  x  109  cm./sec.  without  any  indi- 
cation of  a  change  in  the  value  of  e/m. 

Lenard*  has  also  made  some  very  interesting  experiments  on 
the  effect  of  an  external  electric  field  in  accelerating  or  retarding 
the  motion  of  the  ions.  The  apparatus  used  for  this  purpose  is 
shown  in  Fig.  29. 


Q 


Fig.  29. 

The  rays  after  coming  through  the  window  A  pass  through  small 
holes  in  two  parallel  circular  metallic  plates  G^  and  C2 ;  of  these  C^ 
is  always  kept  connected  with  the  earth  while  (72  is  charged 
positively  or  negatively  by  means  of  an  electrical  machine ;  after 
leaving  this  condenser  the  rays  pass  between  two  plates  M,  used 
for  producing  the  electrostatic  deflection,  on  to  a  screen  $;  the 
dotted  circle  round  M  represents  the  coil  used  for  producing  the 
magnetic  deflection.  The  velocities  of  the  ions  were  measured 
(1)  when  the  plates  of  the  condenser  C^  were  at  the  same 
potential,  (2)  when  they  were  maintained  at  different  potentials;  it 
was  found  that  when  .the  plate  (72  was  negatively  electrified  the 
velocity  in  case  (2)  was  less  than  that  in  (1)  while  when  the  plate 
(72  was  positively  electrified  it  was  greater ;  if  vt  is  the  velocity  of 
the  ions  in  case  (1),  v2  that  in  case  (2),  then  assuming  that  the 

9 

*  Lenard,  Wied.  Ann.  xlv.  p.  504,  1898. 


52] 


THE    CHARGE   TO    THE    MASS   OF   AN    ION. 


97 


whole  change  in  the  energy  is  due  to  the  action  of  the  electric 
field  we  have 

±m(vJ-vS)=eV. (1), 

where  V  is  the  potential  difference  between  the  plates,  V  being 
taken  positive  when  C2  is  at  a  higher  potential  than  Cl.  The 
results  of  Lenard's  experiments  are  given  in  the  following  table, 
the  fourth  column  contains  the  value  e/m  calculated  by  equation 

(i). 


*>!  (cm.  /sec.) 

v2(cm./sec.) 

V  (electromagnetic 
units) 

elm 

•7   xlO10 

•35  x  10l° 

-291x  1010 

6'2  x  106 

•68  x  1010 

•34  x  1010 

-210xl010  f 

8-1  xlO6 

•62  *  1010 

•89  x  1010 

+  291  xlO10  / 

6-9  xlO6 

•77  x  1010 

•47  x  1010 

-  291  x  1010 

6'4  xlO6 

•79  xlO10 

1-0   x  1010 

.+291xl010 

6-6  x  106 

•88  x  1010 

1-07  x  1010 

+  291xlOl° 

6-5  x  10« 

The  constancy  of  the  value  of  e/m  is  a  strong  confirmation  of 
the  truth  of  the  theory  that  the  rays  are  charged  particles  in 
rapid  motion. 


Method  of  determining  the  value  of  e/m  and  v  by  measuring 
the  energy  carried  by  the  cathode  rays. 

52.  Many  other  methods  have  been  employed  to  measure  e/m. 
One  used  by  the  writer*  was  to  measure  the  energy  carried  by 
the  rays.  To  do  this  a  narrow  pencil  of  rays  passed  through  a 
small  hole  in  a  metal  cylinder  and  fell  upon  a  thermo-couple,  the 
couple  was  heated  by  the  impact  of  the  rays,  and  by  measuring  by 
means  of  a  galvanometer  the  rate  at  which  the  temperature  of 
the  junction  increased,  the  amount  of  heat  communicated  to  the 
junction  in  unit  time  was  determined,  let  us  call  this  amount  ^; 
then  if  we  assume  that  all  the  energy  possessed  by  the  cathode 
rays  is  converted  into  heat  we  have 

±Nm&  =  Q, 

where  N  is  the  number  of  ions  which  enter  the  cylinder  through 
the  hole  in  unit  time,  m  is  the  mass  and  v  the  velocity  of  an  ion. 

*  J.  J.  Thomson,  Phil  Mag.  v.  44,  p.  293,  1897. 


98 


DETERMINATION    OF   THE   RATIO    OF 


[52 


If  e  is  the  charge  of  the  ion,  then  in  each  unit  of  time  Ne  units 
of  negative  electricity  will  enter  the  cylinder  ;  the  rate  at  which 
the  negative  charge  increases  can  easily  be  measured  if  the 
cylinder  is  insulated  and  connected  with  an  electrometer,  let  E 
be  the  rate  of  increase  of  the  negative  electricity  inside  the 
cylinder,  then  we  have 


Eliminating  N  from  these  equations  we  get 

1m    .      Q 

—  —  v  =  — 
2  e  V      E' 

If  we  observe  the  magnetic  deflection  produced  by  a  known 
magnetic  field  we  determine  mv/e,  hence  since  we  have  just  seen 

how  to  determine  mtf/e  we  can  deduce  the  values  of  v  and  m/e. 
f* 

The  results  of  experiments  made  in  this  way  are  shown  below. 


Gas 

v 

elm 

Air  

2'4  x  109 

1-1  x  107 

Air  

3-2  x  109 

l'4x  107 

Hydrogen    

2-5  x  109 

1-0x10* 

The  mean  of  the  values  for  e/m  is  1-17  x  107:  this  value  is 
considerably  greater  than  the  one  previously  found,  the  method 
however  is  not  so  reliable  as  the  preceding  one  as  three  measure- 
ments have  to  be  made,  the  magnetic  deflection,  the  heating  effect 
and  the  rate  of  increase  of  the  charge  in  the  cylinder,  instead  of 
two,  the  magnetic  and  the  electric  deflection;  and  it  is  not  merely 
that  the  measurements  are  more  numerous,  they  are  also  more 
difficult,  as  the  measurement  of  the  heating  effect  and  the  rate  of 
increase  of  the  charge  are  much  more  complicated  than  that  of 
the  electrostatic  deflection.  The  conductivity  given  to  the  gas 
by  the  passage  through  it  of  the  cathode  rays  allows  some  of  the 
charge  in  the  cylinder  to  leak  away  and  thus  tends  to  make  the 
observed  value  of  E  smaller  than  .the  true  one ;  in  the  experi- 
ments described  above  efforts  were  made  to  diminish  this  effect 
as  much  as  possible  by  connecting  the  cylinder  to  a  condenser  of 
large  capacity  so  that  the  negative  charge  on  the  ra  should 


53]  THE   CHARGE  TO   THE   MASS   OF  AN   ION.  99 

only  produce  a  small  change  in  the  potential  of  the  cylinder.  We 
may  remark  in  passing  that  the  charges  of  negative  electricity 
carried  by  the  rays  are  very  large,  thus  with  quite  a  small  hole 
(about  1  mm.  in  radius)  in  the  cylinder  the  potential  of  the 
cylinder  would  change  sometimes  as  such  as  5  volts  per  second 
when  exposed  to  the  rays,  even  though  it  was  connected  with 
a  condenser  having  a  capacity  about  '15  microfarad. 

Methods  of  determining  v  and  e/m  from  the  magnetic  deflection 
and  potential  difference  between  the  electrodes  of  the  discharge 
tube. 

53.  These  methods  which  were  first  used  by  Schuster*  in  1890 
are  based  on  the  following  principles.  If  V  is  the  potential  differ- 
ence between  the  terminals  of  the  tube,  then  the  work  done  on  an 
ion  in  passing  from  one  end  of  the  tube  to  the  other  is  Ve,  hence 
the  kinetic  energy  acquired  by  the  ion  can  not  be  greater  than 
Ve,  so  that 

±mv2  $  Ve. 

From  the  observation  of  the  effect  of  the  magnet  on  the 
discharge  (Schuster  measured  the  radii  of  the  circles  which  are 
the  path  of  the  ions  in  a  strong  magnetic  field)  we  know  the 
value  of  mv/e,  let  us  call  this  quantity  q,  then  from  the  preceding 
equation  we  have 

a  2F 

e/m  *  —  . 

To  find  an  inferior  limit  for  e/m,  Schuster  took  v  equal  to  the 
velocity  of  mean  square  of  the  atoms  of  the  gas  in  the  tube ;  calling 
this  velocity  U  we  have 

e/mji  — . 

Substituting  the  values  of  q  and  V  found  in  his  experiments 
Schuster  found  for  air 

e/m  $11  x  105, 

e/m  {  103. 

If  we  assume  that  the  charge  on  the  nitrogen  atom  is  three  times 
that  on  the  atom  of  hydrogen  in  the  electrolysis  of  liquids  and  if 

*  Schuster,  Proc.  Eoy.  Soc.  xlvii.  p.  526. 

7—2 


100          DETERMINATION  OF  THE  RATIO  OF  [54 

m  is  the  mass  of  the  nitrogen  atom,  then  e/m  is  equal  to  2  x  103;  as 
this  is  within  the  limits  for  e/m  previously  found,  Schuster  con- 
cluded that  the  negatively  electrified  particles  in  the  cathode  rays 
in  a  tube  filled  with  nitrogen  are  atoms  of  nitrogen.  We  have 
seen  that  more  recent  investigations  have  led  to  quite  a  different 
conclusion. 

54.  Several  determinations  of  the  values  of  e/m  and  v  have 
been  made  on  the  assumption  that  the  kinetic  energy  possessed  by 
the  ion  is  equal  to  the  energy  that  would  be  acquired  by  the  ion 
in  falling  through  the  potential  difference  V  between  tHe  anode 
and  the  cathode  ;  on  this  assumption  we  have 

\mtf  =  Ve  ....  .......................  (1) 

and  if  q  or  mv/e  is  determined  by  the  magnetic  deflection  we  have 


m 


Determinations  of  e/m  on  this  principle  have  been  made  by 
Kaufmann*  and  subsequently  by  Simon  f.  Kaufmann  found  by 
this  method  that 


-  =  l-86x!07. 
m 


And  Simon,  who  made  a  very  large  number  of  experiments  in 
which  the  potential  difference  between  the  cathode  and  anode 
ranged  from  4860  to  11840  volts,  found  that 

-  =  T865  xlO7. 
m 

The  value  of  e/m  was  found  to  be  independent  of  the  potential 
difference.  A  Wimshurst  machine  was  used  to  produce  the 
discharge  as  this  maintains  a  very  much  more  uniform  potential 
difference  than  an  induction  coil. 

The  values  found  for  e/m  by  this  method  are  larger  than 
those  found  by  the  methods  previously  described  ;  the  method 
is  however  open  to  objection,  for  it  assumes  that  the  kinetic 
energy  of  the  ion  is  equal  to  the  work  done  on  an  ion  starting 
in  the  cathode  itself  and  thus  experiencing  the  maximum  fall  of 

*  Kaufmann,  Wled.  Ann.  v.  61,  p.  544;  62,  p.  596,  1897;  65,  p.  431,  1898. 
t  Simon,  Wled.  Ann.  v.  69,  p.  589,  1899. 


54]  THE   CHARGE   TO  THE   MASS  OF  AN   ION.  101 

potential  possible  in  the  tube,  and  also  that  all  the  work  done 
by  the  electric  field  is  spent  in  increasing  the  kinetic  energy  of 
the  ion  while  none  of  this  energy  is  lost  by  the  collisions  of  the 
ion  with  the  molecules  of  the  gas  through  which  it  passes.  Now 
we  have  no  right  to  assume  without  proof  that  the  ion  starts  from 
the  cathode  itself;  we  shall  see  that,  at  any  rate  when  the 
pressure  is  not  very  low,  large  numbers  of  ions  are  produced  at 
some  little  distance  away  from  the  cathode,  and  as  the  change  of 
potential  in  the  neighbourhood  of  the  cathode  is  very  rapid  such 
ions  would  experience  a  notably  smaller  potential  fall  than  those 
starting  from  the  cathode  itself.  Nor  is  the  fact  that  the  values 
of  ejm  found  by  this  method  are  independent  of  the  potential 
difference  a  conclusive  proof  that  the  ions  under  observation 
started  from  the  cathode.  For  suppose  that  the  distance  from 
the  cathode  of  the  place  from  which  the  greater  part  of  the  ions 
start  is  d,  and  that  V(B  is  the  potential  gradient,  then  the  fall  of 
potential  experienced  by  these  ions  is  V(l—  {3d) ;  now  /3  diminishes 
as  the  pressure  of  the  gases  diminishes  while  d  increases,  so  that 
it  is  quite  possible  that  /3d  is  independent  of  the  pressure  of  the 
gas  (it  would  be  so  if  for  example  0  were  directly  and  d  inversely 
proportional  to  the  pressure);  in  this  case  the  fall  of  potential 
experienced  by  the  ions  would  always  be  a  constant  fraction  of 
the  total  fall  of  potential  in  the  tube,  so  that  the  value  of  e/m 
determined  by  equation  (1)  would  always  bear  a  constant  ratio 
to  the  true  value.  As  the  maximum  potential  difference  used  by 
Simon  was  only  about  1100  volts  the  pressure  could  not  have 
been  very  low  in  his  experiments.  When  the  pressure  of  the  gas 
is  exceedingly  small  the  number  of  collisions  with  the  molecules 
of  a  gas  made  by  an  ion  in  its  journey  down  the  tube  may  be 
so  greatly  reduced  that  but  few  fresh  ions  are  produced  by  the 
collisions  and  in  this  case  the  greater  number  of  the  ions  may  come 
from  the  electrode  itself,  but  even  in  this  case  the  use  of  equation 
(1)  is  not  legitimate,  as  part  of  the  work  may  be  spent  in  tearing 
the  ions  out  of  the  metal  and  only  the  remainder  is  available 
for  increasing  the  kinetic  energy. 

These  considerations  show  that  the  use  of  equation  (1)  leads 
to  an  over-estimate  of  the  kinetic  energy  of  the  ion  and  therefore, 
since  e/m  =  mv2/eq\  the  value  of  e/m  calculated  by  this  method 
will  tend  to  be  too  large. 


102  DETERMINATION   OF   THE   RATIO   OF  [55 

The  method  used  by  Lenard,  and  described  on  page  96,  though 
it  depends  upon  the  same  equations  is  not  open  to  these  ob- 
jections, as  in  this  method  the  potential  difference  which  enters 
into  the  equations  is  applied  to  the  ions  after  they  have  been 
produced  and  started  on  their  path,  and  in  this  case  the  increase 
in  the  kinetic  energy  must  equal  the  work  done  if  we  can  neglect 
the  loss  of  kinetic  energy  of  the  ions  produced  by  collisions  with 
the  molecules  of  the  gas  ;  this  effect  can  be  eliminated  by  working 
at  very  low  pressures  and  varying  the  length  of  path  traversed 
by  the  ion  under  the  electric  field. 

55.  In  January,  1897,  Wiechert*  published  a  determination 
of  the  values  between  which  e/m  must  lie.  The  principles  on 
which  this  determination  is  based  are  as  follows  :  by  measuring 
the  magnetic  deflection  in  a  field  of  known  strength  we  can 

determine  —  v  ;    to  get  a  second   relation   between  m/e   and  v, 
e 

Wiechert  put 


where  V  is  the  difference  of  potential  between  the  electrodes  in 
the  discharge  tube  and  k  an  unknown  quantity  which  cannot  be 
greater  than  unity.  To  get  the  maximum  value  of  v,  and  there- 
fore the  maximum  of  e/m,  k  in  equation  (1)  was  put  equal  to  unity 
To  get  minimum  values  for  v  and  e/m  Wiechert  assumed  that 
the  kinetic  energy  of  the  ions  in  the  cathode  rays  was  greater 
than  that  due  to  a  fall  through  a  potential  difference  equal  to 
the  '  cathode  fall  of  potential.'  The  cathode  fall  of  potential  is 
the  difference  between  the  potential  of  the  cathode  and  that  of  a 
point  on  the  outer  boundary  of  that  dark  space  in  the  discharge 
which  adjoins  the  cathode.  Warburg  has  shown  that  this  cathode 
fall  of  potential  is  independent  of  the  magnitude  of  the  current 
through  the  gas,  of  the  pressure  of  the  gas  and,  within  certain 
limitations,  of  the  nature  of  the  electrodes.  As  its  value  in  air  is 
about  270  volts,  Wiechert  assumed  that  a  minimum  value  for 
kV  was  200  volts.  The  grounds  for  this  assumption  do  not  seem 
obvious  ;  a  priori  it  would  seem  more  probable  that  the  minimum 
value  to  take  for  kV  should  have  been  the  potential  difference, 

*  Wiechert,  Sitzungsber.  d.  Physikal.-okonom.  Gesellsch.  zu  Konigsberg,  i.  Pr.  38, 
p.  1,  1897. 


56]         THE  CHARGE  TO  THE  MASS  OF  AN  ION.          103 

not  between  the  cathode  and  the  outer  boundary  of  this  dark 
space,  but  between  this  boundary  and  the  place  where  the  mag- 
netic deflection  of  the  rays  was  determined,  for  we  know  that  the 
rays  are  fully  developed  at  this  boundary,  and  it  is  by  no  means 
so  certain  that  at  moderate  pressures  they  all  exist  close  to  the 
cathode.  Using  these  assumptions,  however,  Wiechert  found  for 
the  maximum  value  of  e/m  the  value  4  x  107  and  for  the  minimum 
value  4  x  106. 

56.  Wiechert*  has  also  determined  by  direct  measurement 
the  velocity  of  the  ions  in  the  cathode  rays,  using  a  method  first 
applied  by  Des  Coudresf  for  this  purpose.  The  principle  of  the 
method  is  as  follows  :  suppose  that  A  BCD,  A'B'C'D'  are  two  circuits 
traversed  by  very  rapidly  alternating  currents,  such  as  those 
produced  by  the  discharge  of  a  Leyden  jar,  let  us  suppose  that 
the  currents  in  the  two  circuits  are  in  the  same  phase,  and  that 
these  circuits  are  placed  close  to  a  tube  along  which  cathode  rays 
are  passing.  The  currents  in  the  circuits  will  give  rise  to  electric 
and  magnetic  forces  which  will  deflect  the  rays  as  they  pass  by 
the  circuits.  If  the  velocity  of  the  rays  were  infinite,  then  the 
deflections  produced  by  the  two  circuits  on  the  rays  would  be 
equal  and  in  the  same  direction ;  if  however  the  rays  take  a  finite 
time  to  travel  from  one  circuit  to  the  other,  and  if  the  distance 
between  the  circuits  is  adjusted  so  that  this  time  is  equal  to 
half  the  period  of  vibration  of  the  current,  then  the  deflection 
produced  by  the  first  circuit  will  be  equal  and  opposite  to  that 
produced  by  the  second ;  or  if  the  distance  between  the  circuits 
is  such  that  the  time  taken  by  the  rays  to  pass  from  one  circuit 
to  the  other  is  equal  to  one  quarter  of  the  period  of  the  currents, 
then  when  the  effect  produced  by  the  circuit  ABCD  is  a  maximum 
that  produced  by  A'B'C'D'  will  be  zero. 

The  arrangement  used  to  apply  these  principles  to  determine 
the  velocity  of  the  cathode  rays  is  represented  in  Fig.  30  ;  ABCD, 
A'B'C'D'  are  the  circuits  carrying  the  currents  produced  by  the 
discharge  of  the  jars,  C  is  a  concave  cathode,  Blt  Bz  metal  dia- 
phragms perforated  at  the  centre,  G  a  screen  covered  with  some 
material  which  becomes  phosphorescent  when  bombarded  by  the 

*  Wiechert,  Wied.  Ann.,  69,  p.  739,  1899. 

t  Des  Coudves,  Verhandl.  d.  physikal  Gesellsch.  zu  Berlin,  xiv.  p.  86,  1895. 


104 


DETERMINATION    OF   THE   RATIO   OF 


[56 


cathode  rays.     If  is  a  horse-shoe  magnet  which  deflects  the  rays 
from  the  hole  in  the  diaphragm  Blt  so  that  when  no  currents  are 


Fig.  30. 

passing  through  ABCD,  A'B'C'D'  the  cathode  rays  are  stopped  by 
the  diaphragm  and  the  phosphorescent  screen  remains  dark.  When 
a  current  passes  through  ABCD  the  pencil  of  cathode  rays  is  de- 
flected and  swings  backwards  and  forwards  like  a  pendulum,  if 
during  the  swing  the  pencil  strikes  the  hole  in  B±  some  of  the 
rays  will  get  through  B±  and  B2,  and  the  screen  G  will  be  illumi- 
nated. The  brightness  of  the  illumination  will  be  greatest  when 
the  hole  in  BI  is  just  at  the  extremity  of  the  swing  caused  by 
the  current  in  ABCD,  for  in  this  case  the  pencil  is  momentarily  at 
rest,  and  the  time  the  pencil  remains  on  the  opening  is  therefore 
a  maximum.  If  there  is  no  current  in  A'B'C'D'  the  position 
of  the  phosphorescent  spot  on  the  screen  will  be  on  the  line 
joining  the  holes  in  the  two  diaphragms ;  if  a  current  in  the  same 
phase  as  that  through  ABCD  is  passing  through  A'B'C'D',  then 
since  the  cathode  rays  that  reach  the  diaphragm  are  displaced 
upwards  by  the  current  in  ABCD,  they  wrill  be  similarly  displaced 
by  that  in  A'B'C'D',  and  the  phosphorescent  patch  will  be  above 
the  line  joining  the  holes  in  the  diaphragm,  while  if  the  current 
in  A'B'C'D'  is  in  the  opposite  phase  the  patch  will  be  displaced 


56]  THE   CHARGE   TO   THE    MASS   OF    AN    ION.  105 

downwards,  the  direction  of  the  displacement  of  the  patch  will 
be  reversed  by  reversing  the  poles  of  the  magnet.  If  however 
the  phases  of  the  currents  in  ABCD,  A'B'G'D'  differ  by  a  quarter  of 
a  period,  then  when  the  vertical  displacement  due  to  ABCD  is 
a  maximum  that  due  to  A'B'G'D'  will  be  zero,  and  the  vertical 
distribution  of  the  light  on  the  screen  G  will  not  be  affected  by 
reversing  the  magnet  M.  We  can  ensure  that  the  rays  which 
get  through  the  opening  in  Bl  are  those  which  are  passing  when 
the  vertical  displacement  due  to  the  current  in  ABGD  is  greatest, 
by  gradually  increasing  the  deflection  of  the  rays  by  moving  the 
magnet  M ;  when  we  have  got  M  into  such  a  position  that  any 
further  increase  in  the  deflection  prevents  any  rays  from  reaching 
the  screen,  we  know  that  only  those  which  suffer  the  maximum 
deflection  come  under  the  action  of  A'B'G'D' ;  if  then  we  move 
A  B  G'D  into  such  a  position  that  the  vertical  distribution  of  phos- 
phorescence on  the  screen  is  not  affected  by  reversing  M,  we 
know  that  when  the  rays  are  passing  A'B'G'D'  the  current  in  this 
circuit  differs  in  phase  by  a  quarter  period  from  the  phase  of  the 
current  in  ABGD  when  the  rays  were  passing  that  circuit.  If  the 
circuits  ABGD,  A'B'G'D'  are  arranged  so  that  the  currents  in  them 
are  simultaneously  in  the  same  phase,  we  know  that  the  rays  must 
have  taken  a  time  equal  to  one  quarter  of  a  period  of  the  currents 
to  pass  from  ABGD  to  A'B'G'D'.  The  period  of  the  currents  can 
be  determined  by  Lecher's  method*,  hence  knowing  the  distance 
between  the  circuits  we  can  determine  the  velocity  of  the  rays. 

The  arrangement  used  to  carry  out  this  method  is  represented 
in  Fig.  31.  GG  are  two  pairs  of  parallel  plates,  the  upper  pair 
of  plates  are  connected  with  the  spark  gap  F,  which  is  also  con- 
nected with  the  terminals  of  an  induction  coil,  the  lower  pair  of 
plates  are  connected  symmetrically  with  the  circuits  ABCD, 
A'B'C'D.  The  cathode  rays  are  produced  by  a  system  in  electrical 
connection  with  that  producing  the  alternating  currents.  L  and  L 
are  two  Leyden  jars  whose  outer  coatings  are  connected  with  the 
extremities  of  the  spark  gap  F,  the  inner  coatings  of  the  jars 
are  connected  with  the  primary  coil  of  a  high  tension  transformer, 
the  secondary  coil  of  which  is  connected  with  the  anode  and 
cathode  of  the  discharge  tube.  In  order  to  prevent  the  rays 
being  scattered  to  the  walls  of  the  tube  during  their  passage 

*  Lecher,  Wied.  Ann.  91,  p.  850,  1890. 


106 


DETERMINATION   OF   THE   RATIO   OF 


[56 


from   one   circuit  to   another   a   magnetising   spiral   was   wound 
round  the  tube  producing  a  magnetic  force  parallel  to  the  length 


of  the  tube;  this  concentrated  the  rays  along  the  axis  of  the  tube 
and  made  the  observations  easier.  With  this  contrivance  it  was 
found  possible  not  merely  to  find  a  position  of  A'B'C'D',  when  the 
currents  differed  by  a  quarter  of  a  period,  when  the  rays  passed 
through  them,  but  to  find  the  second  position  when  they  differed 
by  three-quarters  of  a  period. 

If  X  is  the  distance  between  the  circuits  when  they  differ  by 
a  quarter  period,  L  the  wave-length  of  the  electrical  waves  pass- 
ing through  these  circuits,  v  the  velocity  of  the  rays,  and  V  the 
velocity  of  light,  then 

v_       \_ 
V 


Thus,  in  one  experiment,  L  =  940  cm.,  X  =  39,  hence  v  is  about 
5  x  109.  The  pressure  was  between  |  and  J  of  a  millimetre. 
v  being  determined,  we  get  e/m  from  the  value  of  mv/e,  which 
is  got  by  measuring  the  magnetic  deflection  of  the  rays.  The 
determination  of  v  by  this  method  is  difficult  and  we  cannot 
expect  a  high  degree  of  accuracy.  As  the  result  of  his  experi- 


57]  THE   CHARGE   TO   THE    MASS   OF   AN    ION.  107 

ments,  Wiechert  came  to  the  conclusion  that  the  value  of  e/m 
is  between  1-55  x  107  and  1-01  x  107.  The  most  probable  value 
he  gives  as  1'26  x  107. 

Determination  of  e/m  for  the  negative  ions  produced  when  ultra- 
violet light  falls  on  a  metal  plate,  the  gas  through  which  the 
ions  pass  being  at  a  very  low  pressure. 

57.  The  writer*  determined  the  values  of  e/m  for  the  negative 
ions  produced  by  the  incidence  of  ultra-violet  light  on  a  metal  plate 
by  the  following  method.  It  is  proved  on  page  88  that  when 
an  ion  starts  from  rest  from  the  plane  x  =  0,  at  the  time  t  =  0, 
and  is  acted  on  by  a  uniform  electric  field  of  strength  X,  parallel 
to  the  axis  of  #,  and  by  a  uniform  magnetic  force  H,  parallel 
to  z,  the  position  of  the  particle  at  the  time  t  is  given  by  the 
equations 


—  cos    - 
e    a.*  (  \m 

m    X   (  e  .    /  e   TT\ 

y=~     r/o  I"  Ht  -  sin    —  Ht  I 

e    /:/-  (m  \m       / 

where  x  and  y  are  the  coordinates  of  the  ion.  The  path  of  the 
ion  is  thus  a  cycloid,  and  the  greatest  distance  the  ion  can  get 
from  the  plane  x  =  0  is  equal  to  2mX/eH2. 

Suppose  now  that  we  have  a  number  of  ions  starting  from 
the  plane  x  =  0,  and  moving  towards  the  parallel  plane  x  —  a, 
supposed  to  be  unlimited  in  extent,  if  a  is  less  than  2mX/eH* 
all  the  ions  which  start  from  x  =  0  will  reach  the  plane  x—a, 
while  if  a  is  greater  than  2mX/eH2  none  of  the  ions  will  reach 
this  plane.  If  x  =  0  is  a  zinc  plate  illuminated  by  ultra-violet 
light,  and  thus  the  seat  of  a  supply  of  negative  ions,  and  x  =  a 
a  metal  plate  connected  with  an  electrometer,  then  when  a 
definite  electric  intensity  is  established  between  the  plates,  so 
that  the  number  of  ions  which  leave  the  plate  in  unit  time  is 
fixed,  and  if  a  is  less  than  2Xm/eH2,  all  the  ions  which  start 
from  x  =  0  will  reach  the  plane  x  =  a.  Thus  the  rate  at  which 
the  plate  connected  with  the  electrometer  receives  a  negative 
charge  will  be  the  same  when  there  is  a  magnetic  force  acting 
across  the  plate  as  when  there  is  no  such  force.  If  however 

*  J.  J.  Thomson,  Phil.  Mag.  v.  48,  p.  547,  1899. 


108  -DETERMINATION    OF   THE    RATIO    OF  [57 

a  is  greater  than  2Xm/eH2,  then  no  ion  which  starts  from  x  =  0 
will  reach  the  plane  x  =  a,  and  this  plate  will  not  receive  any 
negative  charge :  so  that  in  this  case  the  magnetic  field  entirely 
stops  the  supply  of  negative  electricity  to  the  plate  connected 
with  the  electrometer.  Thus,  on  this  theory,  if  the  distance 
between  the  plates  is  less  than  a  certain  value,  the  magnetic 
force  produces  no  effect  on  the  rate  at  which  the  plate  connected 
with  the  electrometer  receives  a  negative  charge,  while  when  the 
distance  is  greater  than  this  value  the  magnetic  force  entirely 
stops  the  supply  of  negative  electricity  to  the  plate.  The  actual 
phenomena  are  not  so  abrupt  as  this  theory  indicates.  We  find 
in  practice  that  when  the  plates  are  near  together  the  magnetic 
force  produces  only  an  exceedingly  small  effect,  and  this  an 
increase  in  the  rate  of  charging  of  the  plate.  On  increasing 
the  distance  between  the  plates,  we  come  to  a  stage  where  the 
magnetic  force  produces  a  very  great  diminution  in  the  rate  of 
charging;  it  does  not.  however,  stop  it  abruptly,  as  there  is 
a  considerable  range  in  which  the  magnetic  field  diminishes  but 
does  not  entirely  stop  the  supply  of  negative  electricity  to  the 
plate.  At  still  greater  distances  the  current  to  the  plate  under 
the  magnetic  force  is  quite  insignificant  compared  with  the 
current  when  there  is  no  magnetic  field.  We  should  get  this 
gradual  instead  of  abrupt  decay  of  the  current,  if  the  ions, 
instead  of  all  starting  from  the  plane  x  =  0,  started  from  a  layer 
of  finite  thickness  t ;  in  this  case  the  first  ions  which  failed  to 
reach  the  plate  would  be  those  which  started  from  x  —  0,  this 
would  occur  when  a  =  2mX/eHz,  some  ions  would  however  con- 
tinue to  reach  the  plate  until  a  =  t  +  2mX/eH2.  Thus  if  we 
measure  the  distance  between  the  plates  when  the  magnetic 
force  first  begins  to  retard  the  current,  we  can,  if  we  know  the 
values  of  X  and  H,  determine  the  value  of  e/m.  The  finite  thick- 
ness of  the  layer  from  which  the  ions  start  may  be  explained  by 
the  use  of  a  principle  which  we  shall  find  of  great  importance 
in  many  other  phenomena  connected  with  the  discharge  of  elec- 
tricity through  gases :  it  is  that  when  ions  move  through  a  gas 
with  a  velocity  exceeding  a  certain  limit,  the  ions  by  their 
collisions  with  the  molecules  of  the  gas  through  which  they 
move  produce  fresh  ions.  Thus  when  the  negative  ions  wrhich 
start  from  the  metal  surface  acquire  under  the  electric  field 
a  certain  velocity  they  will  produce  new  ions,  and  thus  the  ion- 


58] 


THE    CHARGE   TO   THE    MASS   OF   AN    ION. 


109 


isation  will  not  be  confined  to  the  metal  plate  but  will  extend 
through  a  layer  of  finite  thickness. 

In  using  this  method  of  determining  e/m  it  is  necessary  to 
have  the  gas  between  the  plates  at  a  very  low  pressure,  so  low 
that  the  mean  free  path  of  the  ion  is  at  least  comparable  with 
the  distance  between  the  plates ;  if  this  is  not  the  case  the  resist- 
ance offered  to  the  motions  of  the  ions  by  the  viscosity  of  the  gas 
prevents  the  preceding  investigation  from  being  applicable. 

The  mean  value  of  e/m  found  in  these  experiments  was 
7  3  x  106.  It  thus  agrees  very  well  with  the  value  7'6  x  106  found 
for  the  same  quantity  for  the  carriers  of  the  negative  electricity  in 
the  cathode  rays :  and  proves  that  the  carriers  of  electricity  in  the 
two  cases  are  the  same,  or,  as  we  may  express  it,  that  a  metal 
plate  emits  cathode  rays  when  illuminated  by  ultra-violet  light. 

58.  Lenard*  in  1900  also  measured  the  value  of  e/m  in  the 
case  of  the  discharge  of  negative  electricity  through  gas  at 
a  very  low  pressure  from  a  cathode  illuminated  by  ultra-violet 
light.  The  arrangement  he  used  is  represented  in  Fig.  32.  A  is 


Fig.  32. 

an  aluminium  plate  on  which  the  ultra-violet  light  shines :  this 

light   comes   from    a   spark   between   zinc   electrodes  and  enters 

the  tube   through   the  quartz  window  B.      E  is  another  metal 

*  Lenard,  Drudes  Annalen,  ii.  p.  359,  1900. 


110 


DETERMINATION    OF   THE   RATIO    OF 


[58 


electrode  perforated  in  the  middle  and  connected  with  the  earth, 
it  shields  the  right-hand  part  of  the  apparatus  from  the  electro- 
static action  of  the  charged  electrode  A.  D  and  C  are  electrodes 
which  can  be  connected  with  an  electrometer.  When  A  is  charged 
up  a  stream  of  negative  electricity  goes  through  the  opening  in 
E,  and  striking  against  the  plate  D,  charges  up  the  electrometer 
with  negative  electricity.  If  the  electrometer  be  connected  with  C 
instead  of  with  D,  it  will  not  however  receive  any  charge.  We  can 
however  give  C  a  charge  by  deflecting  the  stream  of  negative 
ions  by  a  magnet  until  they  strike  against  C.  As  we  still  further 
increase  the  magnetic  field  the  ions  will  be  deflected  by  the  field 
past  C,  and  the  charge  communicated  to  C  will  fall  off  rapidly. 
The  amount  of  negative  electricity  received  by  the  electrodes  D  and 
C  respectively,  as  the  magnetic  force  is  increased,  was  in  Lenard's 
experiments  represented  by  the  curves  in  Fig.  33.  The  ordinates 
are  the  charges  received  by  the  electrodes  and  the  abscissae  the 
values  of  the  magnetic  force.  s  The  curve  to  the  left  is  for  the 


Fig.  33. 

electrode  D,  that  to  the  right  for  C.  Since  the  negative  ions  are 
not  exposed  to  any  electric  field  in  the  part  of  the  tube  to  the 
right  of  E  their  paths  in  this  region  under  a  constant  magnetic 
field  will  be  circles  whose  radii  are  equal  to  mvfeH.  Now  C  will 
receive  the  maximum  charge  when  the  circle  with  this  radius 
passing  through  the  middle  of  the  hole  in  E,  and  having  its 
tangent  at  this  point  horizontal,  passes  also  through  the  middle 
of  the  electrode  C.  The  radius  R  of  this  circle  is  fixed  by  the 
relative  positions  of  E  and  C.  Hence,  if  we  measure  H  when 
C  receives  its  maximum  charge,  we  have 


R  = 


mv 


.(1). 


The  velocity  is  determined  by  the  assumption  that  the  work 


60]  THE   CHARGE   TO   THE   MASS   OF  AN   ION.  Ill 

done  by  the  electric  field,  when  the  ion  passes  from  A  to  E,  is 
spent  in  increasing  the  kinetic  energy  of  the  ion  (we  have  already 
considered  on  page  100  the  objections  which  may  be  raised  against 
this  assumption) :  this  leads  to  the  equation 

^mv^  =  Ve (2), 

where  V  is  the  potential  difference  between  A  and  E.  From 
equations  (1)  and  (2)  the  values  of  e/m  and  v  can  be  determined. 
In  this  way  Lenard  found  that  e/m  for  the  negative  ions  produced 
by  the  action  of  ultra-violet  light  in  a  gas  at  a  very  low  pressure 
is  equal  to  I'lo  x  107. 

59.  Value  of  e/m  for  the  negative  ions  produced  by  an  incan- 
descent wire. 

A  metal  wire  when  raised  to  a  white  heat  in  a  gas  at  a  very 
low  pressure  gives  out  negative  ions;  the  writer*  has  determined 
the  value  of  e/m  for  the  negative  ions  given  out  by  an  incan- 
descent carbon  filament  in  hydrogen  at  a  very  low  pressure.  The 
method  used  was  the  same  as  that  used  by  him  to  determine  the 
value  of  e/m  for  the  ions  produced  by  the  action  of  ultra-violet 
light,  and  which  has  already  been  described  on  page  107.  The 
value  of  e/m  found  in  this  way  was  8'7  x  106,  which  agrees  within 
the  errors  of  experiment  with  the  values  found  for  e/m  for  the 
ions  in  the  cathode  rays,  and  for  those  produced  by  the  action  of 
ultra-violet  light. 

60.  Value  of  e/m  for  the  negative  ions  emitted  by  radio-active 
substances. 

It  has  been  shown  by  M.  and  Madame  Curie f  that  the  radio- 
active substance  radium  -emits  negative  ions.  The  velocity  of  these 
ions  and  the  value  of  e/m  have  been  determined  by  BecquerelJ:. 
The  method  he  employed  was  to  measure  the  deflections  of  the 
rays  produced  by  an  electrostatic  and  also  by  a  magnetic  field. 
The  experiments  were  made  at  atmospheric  pressure,  and  the 
resistance  offered  to  the  motion  of  the  ions  by  the  gas  through 
which  they  pass  was  neglected :  this  would  not  be  justifiable  in 

*  J.  J.  Thomson,  Phil.  Mag.  v.  48,  p.  547,  1899. 
t  M.  et  Mme.  Curie,  Comptes  Rendus,  t.  130,  p.  647. 

£  Becquerel,  Rapports  pre'sentts  au  Congrls  International  de  Physique  a  Paris, 
t.  iii.  p.  47,  1900. 


112  DETERMINATION   OF   THE   RATIO   OF  [60 

the  case  of  the  ions  we  have  hitherto  been  considering,  but  as 
the  ions  emitted  by  radium  are  very  much  more  penetrating  than 
those  we  have  hitherto  considered,  and  are  able  to  travel  as  far 
through  a  gas  at  atmospheric  pressure  as  other  kinds  of  ion 
travel  through  a  gas  at  a  very  low  pressure,  we  shall  probably  get 
approximately  the  right  values  for  e/m  and  v  for  the  radium  ions 
even  if  we  neglect  the  resistance  of  the  gas.  The  radium  was 
placed  below  two  parallel  vertical  metal  plates,  about  3*5  cm.  wide 
and  1  cm.  apart ;  above  these  metal  plates  was  a  horizontal  photo- 
graphic plate  protected  by  a  covering  of  black  paper  from  the  action 
of  light ;  a  thin  slip  of  mica,  symmetrically  situated  with  respect  to 
the  metal  plates,  was  placed  over  the  radium,  this  cast  a  shadow 
on  the  photographic  plate  which  when  the  metal  plates  were  at 
the  same  potential  was  at  the  middle  of  the  field ;  when  a  great 
difference  of  potential,  10,200  volts,  was  maintained  between  the 
plates  the  position  of  this  shadow  was  displaced  towards  the 
positive  plate.  Consider  an  ion  passing  between  the  plates,  then 
if  I  is  the  length  of  its  path  between  the  plates,  F  the  electric 
force  acting  upon  it,  the  displacement  of  the  ion  parallel  to  the 
lines  of  electric  force  when  it  leaves  the  region  between  the  plates 

is  -x   —   — ,  and  its  direction  of  motion  is  displaced  through  an 
2m   v2 

Fe   I 

angle  tan"1  -     —  ,  hence  if  h  is  the  vertical  distance  of  the  photo- 
m    v 

graphic  plate  above  the  upper  edge  of  the  parallel  metal  plate, 
the  point  where  the  ion  strikes  the  plate  will  be  deflected  through 
a  space  8  parallel  to  the  line  of  electric  force,  where  8  is  given 
by  the  equation 

.      I  Fe   I2      ,Fe    I 

o  =  «  -       ~i  +  h  —   -»- 

z   77i    v2         m    v2 

=  Fe    I   (I 
m    \ 

The  magnetic  deflection  was  found  in  the  following  way :  a 
small  quantity  of  radium  was  placed  in  a  little  lead  saucer  on 
a  photographic  plate ;  as  none  of  the  rays  from  the  radium  reach 
the  plate  the  latter  is  not  affected ;  if  however  a  strong  magnetic 
field,  with  the  lines  of  force  parallel  to  the  plate,  acts  on  the 
negative  ions  coming  from  the  radium,  these  will  be  bent  round 
and  will  strike  the  plate,  producing  a  photograph. 


60]          THE  CHARGE  TO  THE  MASS  OF  AN  ION.         113 

To  find  the  boundary  of  this  photograph,  let  us  take  the 
plane  of  the  photographic  plate  as  the  plane  of  xyy  the  magnetic 
force  H  being  parallel  to  x ;  the  equations  of  motion  of  an  ion  are 

d?x  d*y       „.  dz  d2z  _  dy 

md<*  =  0'       md?  =  HeTt>        mM=-Hedt> 

the  solutions  of  these  equations  are,  if  a)  =  He/m,  and  u,  A,  B 
are  constants, 

x  =  ut, 

y  =  A  (1  —  cos  cot)  -f  B  sin  wt, 

z  =  A  sin  cot  +  B  (cos  wt  —  1). 
If  v  and  w  are  the  values  of  dy/dt,  dzjdt  when  t  =  0,  we  have 

y  =  —  (1  —  cos  at)  +  —  sin  cot, 

z  =  —  sin  wt  H (cos  &>£  —  1 ) ; 

w  a) 

when  the  ion  strikes  the  plane  we  have  2  =  0,  hence 

w 
tan  -kwt  =  ~  . 

v 

Now  if  the  ion  is  projected  so  as  to  make  an  angle  6  with 
the  direction  of  the  magnetic  force,  and  if  the  plane  through  the 
direction  of  projection  and  the  axis  of  x  makes  an  angle  <£  with 
the  plane  of  xz,  we  have,  if  V  is  the  velocity  of  projection, 

u  =  V  cos  6,    v  =  V  sin  6  sin  <£,    w  =  V  sin  6  cos  </>, 
hence  tan  ^a>t  =  cot  < 

=  tan       - 


thus  (tit  =  7T  —  2(f). 

Substituting  this  value  for  t,  we  find,  if  f  and  77  are  the  co- 
ordinates of  the  point  where  the  ion  strikes  the  photographs 
plate 

V  cos  6 

0) 

2Fsin0  cc 


Thus,  for  the  particles  projected  in  a  plane  through  the  axis 
of  x,  the  locus  of  the  points  where  they  strike  the  plate  will  be 
T.  G.  8 


114  DETERMINATION    OF   THE    RATIO    OF  [60 

an  ellipse  whose  semi-axes  are   —     -  ^  and    — (^  ~    9_)  $     por 

&)  GO 

the  particle  projected  in  the  plane  of  xz,  the  semi-axes  of  the 
ellipse  are  2V/to  and  TrV/w.  An  example  of  such  an  ellipse  is 
shown  in  Fig.  .34  which  is  copied  from  a  photograph  by  Becquerel. 


Fig.  34. 

By  the  measurement  of  the  axes  of  the  ellipse  we  can  deter- 
mine F/ct),  i.e.  Vm/eH.  As  the  radium  emits  ions  having  velocities 
extending  over  a  considerable  range,  the  impression  on  the  plate 
is  not  the  arc  of  a  single  ellipse,  but  a  band  bounded  by  the 
ellipses  corresponding  to  the  smallest  and  greatest  velocities  of 
the  ions.  Becquerel  took  photographs  when  the  ions  from  the 
radium  went  (1)  through  the  air  at  atmospheric  pressure,  and 
(2)  through  air  at  very  low  pressure  ;  the  photographs  were  found 
to  be  identical,  in  fact  one-half  of  the  photograph  represented 
in  Fig.  34  is  produced  by  ions  going  through  air  at  atmospheric 
pressure,  and  the  other  half  by  ions  going  through  air  at  a  very 
low  pressure.  The  identity  of  the  results  in  the  two  cases  justifies 
us  in  our  neglect  of  the  resistance  of  the  air. 

A  simpler  method  than  the  electrostatic  method  used  by 
Becquerel  to  get  a  second  relation  between  v  and  e/m,  would  be 
to  place  the  radium  on  a  photographic  plate  in  a  little  tube 
so  that  all  the  ions  start  at  right  angles  to  the  plate.  A  uniform 
magnetic  field  acts  parallel  to  the  plate,  and  above  the  photo- 
graphic plate  and  parallel  to  it  is  a  metal  plate  which  is  connected 
with  an  electric  machine ;  when  this  plate  is  charged  with  elec- 
tricity there  will  be  a  strong  electric  field  acting  on  the  ion 
parallel  to  its  direction  of  projection  and  at  right  angles  to  the 
magnetic  force.  If  photographs  are  taken  (1)  with  the  plate 
uncharged,  (2)  with  the  plate  charged,  the  two  photographs  will 
give  us  a  simple  method  of  finding  v  and  e/m.  For  let  us  suppose 
that  all  the  ions  have  the  same  velocity  V,  the  distance  *2R  of 


60]  THE   CHARGE   TO   THE   MASS   OF   AN   ION.  115 

the  image  from  the  radium  in  the  first  photograph  is  given  by 
the  equation 

m    V 

-K  =  —      -pp  . 

e    H 

To  find  the  distance  of  the  image  in  the  second  photograph, 
let  us  take  the  same  axes  as  before,  and  let  Z  be  the  electric 
force  at  right  angles  to  the  plate,  then  the  equations  of  motion 
of  an  ion  are 

d2z  dy 

m  —  =  Ze  -  H  e  -*-  , 
dt2  dt 

d*        „  dz 


The  solution  of  these  equations,  when  z,  y,  dy/dt  vanish  when 
t  =  0,  is 

Z  (      smcot\      V 
V  =  jf  (t  --     -+  —  (1  -  cos  cot), 
H  \          co     )      co 

Z  V  . 

(1  —  cos  tot)  H  —  sin  cot, 

^  CO 


where  V  is  the  velocity  of  projection  of  the  ion. 

When  the  ion  strikes  the  photographic  plate  z  —  0,  hence 

*•"*"*—  j/ir 

Substituting  this  value  of  t  iu  the  expression  for  y  we  find,  if  Rl 
is  the  distance  from  the  radium  of  the  point  at  which  the  ion 
strikes  the  plate, 


but  2  V/to  =  R,  where  R  is  the  distance  from  the  radium  of  the 
point  of  return  of  the  ion  when  the  upper  metal  plate  is  not 
charged,  hence  we  have 

Rl  —  R  =  jg.  t, 

R,-R    V 
°t=  - 


y 
hence  since  tan  \  cot  —  — 


8—2 


116  DETERMINATION   OF   THE   RATIO   OF  [60 

-R     V  V 


we  have  tan 


an  equation  by  which  we  can  determine  the  value  of  V/(Z/H) 
When  V  is  known,  e/m  can  be  determined  from  the  value  of  R. 

When  Z/H  is  small  compared  with  V  an  approximate  solution 
of  equation  (1)  is 


Becquerel  did  not  use  this  method  of  determining  V,  but  the 
electrostatic  method  previously  described;  the  latter  method  is 
not  however  in  many  respects  so  convenient  as  the  one  just  given. 

As  the  result  of  his  experiments  Becquerel  found  for  one  set 
of  rays  given  out  by  the  radium 

v  =  l'Q  xlO10,  e/m  =  I<y, 

thus  the  value  of  e/m  is  the  same  for  these  negatively  charged 
ions  from  radium  as  for  the  ions  in  the  cathode  and  Lenard  rays, 
as  well  as  for  those  produced  by  ultra-violet  light  or  by  in- 
candescent metals.  The  velocity  of  the  ions  is  much  greater  than 
any  we  have  met  with  in  the  case  of  ions  arising  in  other  ways, 
amounting  as  it  does  to  more  than  half  the  velocity  of  light  ; 
the  ions  chosen  by  Becquerel  for  this  experiment  were  by  no 
means  the  fastest  given  out  by  the  radium.  Becquerel  detected 
the  existence  of  others  whose  velocity  was  at  least  half  as  much 
again  as  the  velocity  of  those  he  measured. 

It  may  be  convenient  to  summarise  in  a  table  the  results  of 
the  measurements  of  e/m  made  by  different  observers,  and  with 
ions  produced  in  different  ways. 

It  will  be  seen  from  the  table  that  taking  the  same  method 
the  values  of  e/m  are  practically  the  same  whatever  the  source  of 
the  ions.  We  have  seen  too  that  they  do  not  depend  upon  the 
gas  or  upon  the  nature  of  the  electrodes  ;  thus  in  every  case  in 
which  negative  electrification  has  been  observed  in  gases  at  low 
pressures,  the  value  of  e/m  is  a  constant  quantity  and  is  very 
large,  approximately  1000  times  larger  than  the  largest  value  of 
the  corresponding  quantity  in  the  electrolysis  of  liquid  solutions. 
It  is  to  be  noted  that  these  large  values  of  e/m  for  gases  only 
occur  when  the  pressure  of  the  gas  is  very  low,  when  in  fact  there 


61] 


THE  CHARGE  TO  THE  MASS  OF  AN  ION. 


117 


is   very  little  gas  for  the  ion   to  get   entangled  with;  when  the 
pressure  of  the  gas  is  high,  the   ion   seems  to  act  as  a  nucleus 

TABLE  OF  VALUES  OF  elm. 


Source  of  Ions 

Observer 

Date 

Method  of  Determination 

Value  of  elm 

Cathode  rays 

J.  J.  Thomson 

1897 

Magnetic  and  electrostatic 
deflection 

7-7  x  10« 

" 

J.  J.  Thomson 

1897 

Magnetic  deflection  and 
heating  effect 

1-17  xlO7 

" 

Kaufmann 

1897-8 

Magnetic  deflection  and 
potential  difference 

l-86x!07 

»• 

Simon 

1899 

Magnetic  deflection  and 
potential  difference 

1-865  x  107 

" 

Wiechert 

1899 

Magnetic  deflection  and 
velocity  of  ions 

1-01  x  107— 
1-55  x  107 

Lenard  rays 

Lenard 

1898 

Magnetic  and  electrostatic 
deflection 

6'39xl06 

" 

Lenard 

1898 

Magnetic  deflection  and 
retardation  in  electric 
field 

6-8  x  106 

Ultra-violet 
light 

J.  J.  Thomson 

1899 

Retardation  of  discharge 
by  magnetic  field 

7-6  x  106 

>? 

Lenard 

1900 

Magnetic  deflection  and 
potential  difference 

1-15  x  107 

[ncan  descent 
metals 

J.  J.  Thomson 

1899 

Retardation  of  discharge 
by  magnetic  field 

8-7  x  108 

Radium 

Becquerel 

1900 

Magnetic  and  electrostatic 
deflection 

107  approxi- 
mately 

round  which  the  molecules  of  the  gas  collect ;  the  ion  thus  gets 
loaded  up,  and  the  ratio  of  e/m  is  very  small  compared  with 
its  value  at  lower  pressures. 

61.     Value  of  e/m  for  the  positive  ions. 

The  number  of  determinations  of  the  value  of  e/m  for  the  ions 
which  carry  the  positive  charge  is  small  compared  with  those 
made  for  the  corresponding  quantity  for  the  negative  ions.  The 
first  determination  of  the  value  of  e/m  for  the  positive  ions  was 
made  by  W.  Wien*.  The  positive  ions  he  used  were  those  which 
occur  in  what  are  known  as  '  Canal -strahl en.'  If  an  electric  dis- 
charge passes  between  an  anode  and  a  cathode  perforated  with 


W.  Wien,  Wied.  Ann.  Ixv.  p.  440,  1898. 


118 


DETERMINATION   OF   THE    RATIO   OF 


[61 


a  number  of  holes,  then  behind  the  cathode,  i.e.  on  the  side  of 
the  cathode  opposite  to   the  anode,  pencils  of  light  are  seen  to 


penetrate  through  the  holes  as  in  Fig.  35*,  producing  phosphor- 
escence when  they  strike  the  glass.  These  rays  have  been  shown 
by  Wien  to  consist  of  positively  charged  ions.  He  exposed  a  long 
pencil  of  these  rays  coming  through  a  perforated  iron  cathode  to 
both  an  electrostatic  and  a  magnetic  field,  and  measured  the 
corresponding  deflections ;  from  these  he  deduced  by  the  method 
described  on  page  93,  the  values  of  e/m  and  v,  and  found 

v  =  3'6  x  107  cm./sec.,  while  e/m  —  300. 

The  '  canal-strahlen '  or  positive  rays  are  only  deflected  with 
great  difficulty  by  the  magnetic  field,  and  it  is  necessary  to  use 
very  strong  fields;  this  increases  the  difficulty  of  the  investigation; 
in  Wien's  experiments  the  strength  of  the  field  was  3250.  It  will 
be  seen  from  this  result  that  the  velocity  of  the  positive  ions  is 
very  much  smaller  than  that  of  any  of  the  cathode  rays  hitherto 
measured,  while  the  value  of  e/m  is  of  an  entirely  different  order, 
being  only  about  1/30000  of  the  value  for  the  negative  ion  ;  more- 
over the  value  of  e/m  for  the  positive  ions  in  the  gas  is  of  the  same 
order  of  magnitude  as  the  value  of  e/m  in  the  ordinary  electrolysis 
of  solutions.  Thus  if  m  were  the  mass  of  the  atom  of  iron,  e  the 
charge  carried  by  an  atom  of  hydrogen,  e/m  is  about  200,  or  since 
iron  is  divalent  the  value  of  e/m  for  the  iron  in  the  electrolysis 
of  solutions  is  about  400.  We  have  not  however  sufficient  data 
to  enable  us  to  determine  whether  the  carriers  of  the  positive 
electricity  in  the  'canal-strahlen'  are  the  atoms  or  molecules  of 
the  metal  of  the  cathode  or  of  the  gas  in  the  tube. 

•*  Wehnelt,  Wied.  Ann.  Ixvii.  p.  421,  1899. 


62]  THE   CHARGE    TO   THE    MASS   OF   AN   ION. 


119 


The  energy  in  the  particles  forming  the  positive  rays  or  canal- 
strahlen  is  that  which  they  would  acquire  by  a  fall  through  a 
potential  difference  of  about  16000  volts.  As  we  know  the  charge 
and  the  mass  of  the  particles  forming  the  positive  rays,  we  can 
compare  the  energy  in  the  particles  due  to  this  difference  of 
potential  with  the  mean  energy  possessed  at  any  temperature  by 
the  molecules  of  a  gas,  the  mass  of  the  molecules  being  the  same 
as  that  of  the  particles  in  the  positive  rays;  doing  so  we  find 
that,  even  at  the  highest  attainable  temperature  the  energy  of  a 
molecule  in  the  gas  would  be  quite  insignificant  in  comparison 
with  that  of  a  particle  in  the  positive  rays. 

62.  The  writer  has  determined  the  value  of  e/m  for  the  positive 
ions  by  the  method  described  on  page  106  for  the  determination 
of  the  value  of  e/m  for  the  negative  ions  produced  by  the  action 
of  ultra-violet  light.  The  positive  ions  were  produced  by  raising, 
by  means  of  an  electric  current,  an  iron  wire  to  a  red  heat  in  an 
atmosphere  of  oxygen,  the  pressure  being  very  low.  The  wire 
was  parallel  to  a  metal  plate  connected  with  an  electrometer,  the 
distance  of  the  wire  from  the  plate  was  4  mm.  If  the  wire  was 
charged  positively  the  plate  and  the  electrometer  received  a  posi- 
tive charge,  the  current  passing  between  the  plate  and  the  hot 
wire  being  easily  measured  by  the  electrometer;  if  now  the  space 
between  the  hot  wire  and  the  plate  was  placed  in  a  very  powerful 
magnetic  field,  the  lines  of  force  being  parallel  to  the  plate,  the 
rate  of  leak  from  the  wire  to  the  plate  was  found  to  diminish  if 
the  potential  difference  between  the  wire  and  the  plate  did  not 
exceed  a  certain  value — just  as  in  the  corresponding  case  of 
the  negative  ions  produced  by  ultra-violet  light — but  while  in  the 
latter  case  a  comparatively  feeble  magnetic  force  is  sufficient  to 
diminish  the  current,  it  requires  a  very  powerful  magnetic  force 
to  produce  the  effect  with  the  hot  wire ;  thus  for  example  in  my 
experiments  on  the  positive  ions  I  used  a  magnetic  field  of 
strength  12400  c.G.s.  units,  while  in  the  experiments  on  the 
negative  ones  a  field  of  100  was  amply  sufficient  to  produce  very 
appreciable  effects.  In  the  case  of  the  hot  wire  I  found'  that 
using  a  magnetic  field  of  strength  12400  the  rate  of  leak  was 
less  when  the  magnetic  field  was  on  than  when  it  was  off,  when 
the  potential  difference  between  the  plates  was  less  than  50  volts ; 
when  it  exceeded  this  value  the  rate  of  leak  was  the  same 


120      DETERMINATION   OF   THE    RATIO    OF   THE   CHARGE,    ETC.       [62 

whether  the  magnet  was  on  or  off.  Thus  when  H  =  12400  and 
X  =  50  x  108/'4  the  critical  distance  is  '4  cm.  Hence  by  the 
results  given  on  p.  106  we  have 

_  2  x  50  x  108  m 

~-4  x(12400)27' 

or  -  =  400. 

m 

This  is  about  the  value  for  e/m  for  the  ion  of  iron  in  electrolysis : 
it  does  not  however  prove  that  the  carriers  of  the  positive  elec- 
tricity are  the  atoms  of  iron,  for  if  m  were  the  mass  of  a  molecule 
of  oxygen  and  e  the  charge  on  a  hydrogen  ion  in  the  electrolysis  of 
solutions  e/m  would  be  about  310,  and  the  difficulties  of  the 
experiment  are  so  great  that  we  cannot  say  that  this  result  differs 
from  that  actually  found  by  more  than  the  possible  errors  of  the 
experiment. 

We  see  however  that  for  the  positive  ions  e/m  is  of  the  same 
order  as  in  ordinary  electrolysis  of  solutions,  while  for  negative 
ions  it  is  of  an  entirely  different  order. 

The  effect  of  the  strongest  magnetic  fields  I  have  been  able  to 
use  on  the  current  when  this  is  carried  by  positive  ions  is  very 
much  less  marked  than  the  effect  of  comparatively  weak  fields  on 
the  current  when  it  is  carried  by  negative  ions.  In  the  case  of 
the  positive  ions  the  magnetic  force,  even  in  the  most  favourable 
circumstances,  only  diminishes  the  current,  it  does  not  entirely 
stop  it :  this  points  to  the  conclusion  that  the  carriers  of  the 
positive  charge  are  not  all  of  one  kind,  but  that  sonle  are  much 
heavier  than  others;  thus  in  the  case  of  the  leak  of  positive 
electricity  from  a  hot  platinum  wire  the  study  of  the  effect  of  the 
magnetic  field  on  the  current  leads  us  to  the  conclusion  that 
a  part  of  the  current  is  carried  by  molecules  of  oxygen  and  the 
rest  by  molecules  of  platinum,  or  perhaps  by  aggregates  of  several 
molecules.  The  proportion  between  the  numbers  of  the  different 
kinds  of  carriers  seems  to  vary  very  largely  with  the  temperature 
arid  state  of  the  surface  of  the  platinum. 


CHAPTER  VI. 

DETERMINATION  OF  THE  CHARGE  CARRIED  BY  THE 
NEGATIVE  ION. 

63.     WE  have  seen  that  the  value  of  e/m  for  the  negative  ions 
in  gases  at  a  low  pressure  is  about  a  thousand  times  the  greatest 
value  of  the  ratio  of  the  same  quantities  for  ordinary  electrolytes. 
The  question  at   once  arises,   is  this  due  to  a  difference  in  the 
masses  of  the  ions,  or  to  a  difference  in  their  electrical  charges,  or 
to  both  these  causes :  to  decide  these  points  we  must  determine 
the   value  of  ra  or  e.     The   writer  made  in   1898*  and  1899f 
determinations  of  the  value  of  e  for  the  ions  produced  in  one 
case   by   Rontgen  rays    and  in   the    other  by  ultra-violet   light. 
The  method  was  based  on  the  discovery  made  by  C.  T.  R.  WilsonJ 
(see  Chap.  VII.)  that  gaseous  ions,  whether  positive  or  negative, 
act  as  nuclei  for  the  condensation  of  clouds  even  in  the  absence  of 
dust ;  and  that  if  we  have  a  mass  of  dust-free  gas  containing  ions 
in  a  closed  vessel,  and  cool  the  gas  by  a  sudden  expansion,  then 
a   cloud   will   be    produced  if  the  ratio  of  the    volume   of  the 
gas  after  expansion  to  the   volume  before  is  greater  than   1*25. 
An   expansion   of  this  amount  is  quite    incapable  of  producing 
more   than   very  slight  condensation  in  the  gas  if  it  does  not 
contain  ions.    The  water  condenses  round  the  ions,  and  if  these  are 
not  too  numerous  each  ion  becomes  the  nucleus  of  a  drop  of  water. 
Thus  by  producing  a  sudden  expansion  in  a  gas  containing  ion 
we  can  get  a  little  drop  of  water  round  each  ion  ;  these  drops 
are    visible,    and   we   can   measure   the  rate  at  which   they  fall. 
Sir    George    Stokes   has   shown   that   if  v   is   the   velocity   with 
which  a  drop  of  water  falls  through  a  gas,  a  the  radius  of  the 

*  J.  J.  Thomson,  Phil.  Mag.  v.  46,  p.  528;  1898. 
t  J.  J.  Thomson,  Phil.  Mag.  v.  48,  p.  547,  1899. 
£  C.  T.  K.  Wilson,  Phil.  Trans.,  A,  1897,  p.  265. 


1  20 

J2J  DETERMINATION    OF   THE    CHARGE  [63 

drop,  //,  the  coefficient  of  viscosity  of  the  gas,  and  g  the  acceleration 
due  to  gravity,  then 

-*?' 

thus  if  we  measure  v  we  can  determine  a,  and  hence  the  volume 
of  each  drop.  If  q  is  the  mass  of  water  deposited  from  each 
cubic  centimetre  of  the  gas,  n  the  number  of  the  drops,  we  have 

q  =  n^7ras. 

To  find  q  we  may  proceed  as  follows:  the  gas  after  being  cooled 
by  the  very  rapid  expansion  is  supersaturated  and  moisture  is 
deposited  on  the  ions,  during  the  condensation  of  the  water  heat 
is  given  out  which  warms  the  gas  so  that  the  temperature  of  the 
gas  rises  above  the  lowest  temperature  reached  during  the  ex- 
pansion before  condensation  has  taken  place.  Let  ta  be  the  lowest 
temperature  reached  during  the  expansion,  t  the  temperature 
when  the  drops  are  fully  formed,  then  if  L  is  the  latent  heat  of 
evaporation  of  water,  C  the  specific  heat  of  the  gas  at  constant 
volume,  M  the  mass  of  unit  volume  of  the  gas  after  expansion, 
we  have 

Lq  =  CM(t-  tj  ........................  (1); 

we  neglect  the  heat  required  to  raise  the  temperature  of  the  water 
in  the  gas  in  comparison  with  that  required  to  raise  the  tempera- 
ture of  the  gas  itself.  We  have  further 

2  =  Pi  ~  P> 

where  pt  is  the  density  of  the  water  vapour  before  condensation 
begjfcns,  and  p  the  density  at  the  temperature  t  Substituting  this 
value  for  q  in  equation  (1),  we  get 

-«  ......................  (2). 


Since  p  is  a  known  function  of  t  this  equation  enables  us  to  find 
t  when  t2  is  known. 

If  x  is  the  ratio  of  the  final  to  the  initial  volume  of  the  gas 
and  T  the  temperature  in  degrees  centigrade  of  the  gas  before 
expansion,  then  since  the  mass  of  1  cubic  centimetre  of  air  at  the 
temperature  0°  C.  and  under  a  pressure  of  760  millimetres  of 
mercury  is  '00129  grm.,  we  have 

•00129         273        P_ 
~~  X  760' 


63]  CARRIED    BY   THE    NEGATIVE   ION.  123 

where  P  is  the  initial  pressure  of  the  gas  expressed  in  millimetres 
of  mercury. 

Again,  Pl  =  p-  , 

.  w 

where  p'  is  the  density  of  water  vapour  at  the  temperature  T  before 
expansion  ;  as  the  air  was  saturated  with  water  vapour  at  this 
temperature  p  can  be  obtained  directly  from  the  Tables  of  the 
vapour  pressure  of  water  vapour. 

The  cooling  caused  by  the  adiabatic  expansion  is  determined 
by  the  equation 

4-  71 


For  in  such  an  expansion  pv?  is  constant,  where  p  is  the  pressure 
and  v  the  volume  and  y  the  ratio  of  the  specific  heat  at  constant 
pressure  to  that  at  constant  volume  :  but  pv  =  RO,  where  6  is  the 
absolute  temperature  and  R  a  constant,  hence  we  have  during  an 
adiabatic  expansion 

vy~l  6  =  a  constant  ; 

hence  if  vldl,  vzOz  are  the  initial  and  final  values  of  v  and  0, 
we  have 


or 


Since  7=1-41  this  is  equivalent  to  equation  (3).      From  (3)  we 
determine  t%,  and  then  since 

C  ='167,    Z  =  606, 
equation  (2)  becomes 

167      -00129     273       P    ,. 


As  an  example  of  how  this  equation  is  applied  let  us  take 
a  case  which  occurred  in  one  of  the  experiments.     Here 

^=16°,   P  =  760,   ^=1-36. 
To  get  £2  we  have 

log  27^  +  16  =  -41  log  1-36  =  log  1-134, 
hence  273  + 12  =  254'8,   or  t2  =  -  18°'2. 


124  DETERMINATION   OF   THE    CHARGE  [64 

We  find  from  the  Tables  that  at  16° 

p'  =  -0000135, 
hence  equation  (4)  becomes 

p  =  99'3x  1 0~7  -  2-48  x!0-7(£+ 18-2) (5). 

To  solve  this  equation  we  keep  substituting  various  values  for  t 
until  we  find  one  for  which  the  corresponding  value  of  p  given  by 
(5)  is  the  same  as  the  value  of  the  vapour  pressure  of  water 
at  the  temperature  t.  We  find  by  this  process  of  trial  and 
error  that  the  solution  of  equation  (5)  is  £  =  1'2,  and  the  corre- 
sponding value  of  p  is  51 '5  x  10~7.  Substituting  this  value  for  p 
we  find  q  =  477  x  10~7  grms. 

When  we  know  q  and  a,  n  the  number  of  drops  is  at  once 
determined  by  the  equation 

n  =  q/%7ra*. 

In  this  way  we  can  determine  the  number  of  ions  per  cubic 
centimetre  of  gas.  When  we  know  the  number  of  ions  and  also 
the  velocity  of  the  ions  under  unit  electric  force,  we  can  very  easily 
deduce  the  charge  carried  by  an  ion  by  measuring  the  current 
carried  by  these  ions  across  each  unit  of  area  under  an  electric 
force  E.  For  if  n  is  the  whole  number  of  ions  per  c.c.,  positive  as 
well  as  negative,  U  the  mean  of  the  velocities  of  the  positive  and 
negative  ions  under  unit  electric  force,  the  current  through  unit 
area  is  equal  to 

neEU, 

where  e  is  the  charge  on  the  ion ;  the  electric  force  E  ought  to  be 
so.  small  that  the  current  is  proportional  to  the  electric  force. 
When  this  is  not  the  case  the  number  of  ions  is  diminished  by 
the  action  of  the  electric  field,  and  depends  upon  the  magnitude 
of  the  electric  force. 

We  can  easily  measure  the  current  through  the  ionised  gas 
and  thus  determine  neEU,  and  as  n,  E,  U  are  known  we  can 
deduce  the  value  of  e. 

64.  This  method  was  first  applied  by  the  author  to  determine 
the  charge  on  the  ions  produced  by  Rontgen  rays.  The  method  used 
for  making  the  cloud  and  measuring  the  expansions  is  the  same  as 
that  used  by  C.  T.  R.  Wilson*:  the  apparatus  for  this  and  the 

*  C.  T.  K.  Wilson,  Proc.  Camb.  Phil.  Soc.  ix.  p.  333,  1897. 


641 


CARRIED   BY   THE   NEGATIVE   ION. 


125 


electrical  part  of  the  experiment  is  represented  in  Fig.  36.     The 
gas  which  is  exposed  to  the  rays  is  contained  in  the  vessel  A  • 


this  vessel  is  connected  by  the  tube  B  with  the  vertical  tube  C, 
the  lower  end  of  this  tube  is  carefully  ground  so  as  to  be  in 
a  plane  perpendicular  to  the  axis  of  the  tube,  it  is  fastened 
down  to  the  india-rubber  stopper  D.  Inside  this  tube  there  is 
an  inverted  thin-walled  test  tube  P  with  the  lip  removed  and  the 
open  end  ground  so  as  to  be  in  a  plane  perpendicular  to  the  axis 
of  the  tube.  The  test  tube  slides  freely  up  and  down  the  larger 
tube  and  acts  as  a  piston.  Its  lower  end  is  always  below  the 
surface  of  the  water  which  fills  the  lower  part  of  the  outer  tube ; 
a  tube  passing  through  the  india-rubber  stopper  puts  the  inside  of 
the  test  tube  in  communication  with  the  space  E.  This  space  is 
in  connection  by  the  tube  H  with  a  large  vessel  F  in  which  the 
pressure  is  kept  low  by  a  water-pump.  The  end  of  the  tube  H  is 
ground  flat  and  is  closed  fjy  an  india-rubber  stopper  which  presses 


126  DETERMINATION    OF   THE   CHARGE  [64 

against  it,  the  stopper  is  fixed  to  a  rod,  and  by  pulling  this  rod 
down  smartly  the  pressure  inside  the  test  tube  is  lowered  and  the 
test  tube  falls  rapidly  until  it  strikes  against  the  india-rubber 
stopper.  The  tube  T,  which  can  be  closed  by  a  stop-cock,  admits 
air  into  E  and  allows  us  to  force  the  test  tube  back  into  its  place 
for  another  expansion.  The  tubes  R  and  S  are  for  the  purposes 
of  regulating  the  amount  of  expansion.  To  do  this  the  mercury 
vessel  R  is  raised  or  lowered  when  the  test  tube  is  in  its  lowest 
position  until  the  gauge  G  indicates  that  the  pressure  in  A  is  the 
desired  amount  below  the  atmospheric  pressure.  The  stop-cock  S 
is  then  closed  and  air  is  admitted  into  the  interior  of  the  piston 
by  opening  the  stop-cock  T.  The  piston  then  rises  until  the 
pressure  in  A  differs  from  atmospheric  pressure  only  by  the  amount 
required  to  support  the  weight  of  the  piston  ;  this  pressure  is  only 
that  due  to  a  fraction  of  a  millimetre  of  mercury. 

If  II  is  the  barometric  pressure,  then  Plt  the  pressure  of  the 
air  before  expansion,  is  given  by  the  equation 

p,=n-Tr, 

where  TT  is  the  maximum  vapour  pressure  of  water  at  the  tempera- 
ture of  the  experiment.  The  pressure  of  the  air  P2  after  the 
expansion  is  given  by 

P*-Pi-p, 

where  p  is  the  pressure  due  to  the  difference  of  level  of  the  mercury 
in  the  two  arms  of  the  gauge  G. 

Thus  if  vz  is  the  final  and  Vi  the  initial  volume  of  the  gas 


0!  ~~  P2~  II  —  TT  —  p' 

The  vessel  in  which  the  rate  of  fall  of  the  fog  and  bhe  con- 
ductivity of  the  gas  are  tested  is  at  A.  It  is  a  glass  tube 
36  millimetres  in  diameter  covered  with  an  aluminium  plate  ;  to 
avoid  the  abnormal  ionisation  which  occurs  when  Rontgen  rays 
strike  against  a  metal  surface,  the  lower  part  of  the  aluminium 
plate  is  coated  with  wet  blotting-paper,  and  the  electric  current 
passes  from  the  blotting-paper  to  the  horizontal  surface  of  the 
water  beneath.  The  induction  coil  and  the  focus  bulb  for  the 
production  of  the  Rontgen  rays  are  placed  in  a  large  iron  tank, 
in  the  bottom  of  which  a  hole  is  cut  and  closed  by  an  aluminium 


64]  CARRIED   BY   THE   NEGATIVE   ION.  127 

window.  The  vessel  A  is  placed  underneath  this  window  and 
the  bulb  giving  out  the  rays  some  distance  above  it,  so  that  the  / 
beam  of  rays  escaping  from  the  tank  is  not  very  divergent. 
The  intensity  of  the  rays  can  be  reduced  to  any  required  degree 
by  inserting  leaves  of  tinfoil  or  sheets  of  aluminium  between  the 
bulb  and  the  vessel. 

In  these  experiments  it  is  necessary  to  work  with  very  weak 
rays,  so  that  the  number  of  ions  is  comparatively  small ;  when  the 
number  of  ions  is  large  some  of  them  seem  to  escape  being  caught 
by  the  cloud  produced  by  the  expansion,  for  if  a  second  expansion  be 
produced  (the  ionising  agent  being  cut  off)  a  considerable  cloud  will 
be  formed,  and  it  may  require  several  expansions  before  the  gas  is 
restored  to  the  state  in  which  it  existed  previous  to  the  exposure 
to  the  ionising  agent.  The  cause  of  these  secondary  clouds  has 
not  yet  been  definitely  settled,  but  it  is  possible  that  they  may  be 
due,  partly  at  any  rate,  to  ions  which  have  not  been  caught  by  the 
first  cloud,  and  if  this  were  so  the  number  of  ions  deduced  from 
the  time  of  fall  of  the  cloud  would  be  too  small ;  it  is  therefore 
advisable  to  work  with  such  weak  ionisation  of  the  gas  that  the 
first  cloud  clears  away  all  the  ions. 

To  find  the  current  passing  through  the  gas,  the  tank  and  the 
aluminium  plate  on  the  top  of  the  vessel  A  are  connected  with 
one  pair  of  quadrants  of  the  electrometer,  the  other  pair  of 
quadrants  is  connected  with  the  water  surface  in  the  vessel  A\ 
this  surface  is  charged  up  to  a  known  potential  by  connecting 
it  with  one  of  the  terminals  of  a  battery,  the  other  terminal  of 
which  is  connected  with  the  earth.  After  the  surface  has  been 
charged  it  is  disconnected  from  the  battery  and  the  insulation 
of  the  system  tested  by  observing  whether  there  is  any  leak 
when  the  Rontgen  rays  are  shut  off;  the  insulation  having  been 
found  satisfactory,  the  rays  are  turned  on  and  the  charge  begins 
to  leak  from  the  electrometer;  by  measuring  the  rate  of  leak 
the  quantity  of  electricity  which  in  one  second  passes  through 
the  gas  exposed  to  the  rays  can  be  determined.  For  suppose 
that  in  a  second  the  electrometer  reading  is  altered  by  p  scale 
divisions,  and  that  one  scale  division  of  the  electrometer  corre- 
sponds to  a  potential  difference  V  between  the  quadrants,  and 
that  C  is  the  capacity  of  the  system  consisting  of  the  electrometer, 
the  water  surface  and  the  connecting  wires,  then  the  quantity  of 


128  DETERMINATION   OF  THE   CHARGE  [65 

electricity  which  passes  in  one  second  through  the  gas  exposed 
to  the  rays  is  pVC.  If  n  is  the  total  number  of  ions  positive  as 
well  as  negative  per  cubic  centimetre  of  the  gas,  u0  the  mean  of 
the  velocities  of  the  positive  and  negative  ions  under  a  potential 
gradient  of  a  volt  per  centimetre,  E  the  potential  gradient  in 
volts  per  centimetre  acting  on  the  ionised  gas,  A  the  area  of  the 
water  surface,  the  current  through  the  gas  is  equal  to  Aneu^E\ 
but  as  this  current  is  equal  to  pVC,  we  have 

pVC  =  AneuQE, 

an  equation  by  means  of  which  we  can  determine  ne,  and  as  from 
the  experiments  on  clouds  we  know  the  value  of  n  we  can  at  once 
deduce  the  value  of  e.  Proceeding  in  this  way  the  author  found 
in  1898  that  for  the  ions  produced  by  Rontgen  rays  passing  through 
air,  using  electrostatic  units, 

e  =  6*5  x  10-10  gr>  (cm.)1  (sec.)"1. 

A  similar  series  of  experiments  on  the  ions  produced  by 
Rontgen  rays  passing  through  hydrogen  gave  for  e  the  charge 
on  the  hydrogen  ion  the  value 

67  x  10-10(gr.)*(cm.)^(sec.)-1. 

The  difference  between  this  and  the  value  of  the  charge  on  the 
ion  in  air  is  much  less  than  the  error  of  experiment,  so  that  the 
charges  on  the  ions  are  the  same  in  these  gases.  This  was  shortly 
afterwards  confirmed  by  the  experiments  made  by  Townsend  on 
the  rates  of  diffusion  of  the  ions ;  an  account  of  these  experiments 
has  already  been  given  on  p.  26. 

65.  The  author  in  1901-2  repeated  these  experiments  on  the 
charges  carried  by  the  ions,  making  some  modifications  in  the 
method.  In  the  first  place  the  ionisation  was  produced  by  the  radia- 
tion from  radium  instead  of  by  the  Rontgen  rays  ;  this  was  done  to 
get  a  more  uniform  rate  of  ionisation  than  is  possible  with  Rontgen 
tubes,  the  irregularity  of  which  gave  a  great  deal  of  trouble  in 
the  earlier  investigation.  Secondly,  the  electrometer  used  in  the 
new  experiments  was  much  more  sensitive  than  the  old  one,  the 
new  electrometer  was  of  the  Dolezalek  type  and  gave  a  deflection 
of  20000  scale  divisions  for  a  potential  difference  of  one  volt. 

The  measurements  made  by  C.  T.  R.  Wilson*  (see  Chap.  VII.) 

*  C.  T.  E.  Wilson,  Phil.  Trans,  cxciii.  p.  289. 


66]  CARRIED   BY   THE   NEGATIVE    ION.  129 

show  that  with  expansions  between  T25  and  T3  negative,  and  only 
negative,  ions  act  as  nuclei  for  cloudy  condensation,  while  with 
expansions  greater  than  1*3  both  negative  and  positive  ions  are 
brought  down  by  the  cloud.  It  was  feared  that  when  the  expan- 
sions were  sufficiently  large  to  bring  both  sets  of  ions  into  play  the 
more  active  negative  ions  might  have  a  tendency  to  monopolise 
the  aqueous  vapour,  and  that  therefore  the  whole  of  the  positive 
ions  might  not  be  brought  down  with  the  cloud.  This  fear  was 
found  to  be  justified,  for  with  the  expansion  apparatus  used  in  the 
earlier  experiments  it  was  found  that  with  expansions  greater  than 
1*3  the  number  of  particles  in  the  cloud  formed  in  the  ionised  gas 
was  not,  as  it  should  have  been  if  all  the  ions  had  been  caught  by 
the  cloud,  twice  as  great  as  when  the  expansion  was  less  than  this 
value.  The  apparatus  was  modified  so  as  to  make  the  rate  of 
expansion  very  much  more  rapid  than  in  the  earlier  experiments ; 
with  the  new  apparatus  the  number  of  particles  in  the  cloud  when 
the  expansion  was  greater  than  T3  was  twice  as  great  as  when  the 
expansion  was  less  than  this  value ;  this  confirms  the  view  that 
with  this  apparatus  all  the  ions  are  caught  by  the  cloud.  The 
result  of  a  number  of  determinations  of  e  with  the  new  apparatus, 
using  different  samples  of  radium  and  different  intensities  of 
radiation,  was  that 

e  =  3-4  x  10-10(gr.)*  (cm.)^  (sec.)-1. 

66.  Having  found  the  value  of  e,  let  us  compare  it  with  E  the 
charge  carried  by  the  hydrogen  ion  in  the  electrolysis  of  solutions. 
If  N  is  the  number  of  molecules  in  a  cubic  centimetre  of  a  gas 
at  a  pressure  of  760  mm.  of  mercury  and  at  0°  C.,  then  we  know 
as  the  result  of  experiments  on  the  liberation  of  hydrogen  in 
electrolysis  (see  p.  57)  that 

NE=I'22  x  1010. 

In  treatises  on  the  Kinetic  Theory  of  Gases  (for  example,  0.  E. 
Meyer,  Die  kinetische  Theorie  der  Gase)  it  is  shown  how  by  the 
aid  of  certain  assumptions  as  to  the  nature  and  shape  of  the 
molecules  it  is  possible  to  find  N.  The  values  got  in  this  way 
vary  considerably,  the  best  determinations  of  N  lying  between 
2-1  x  1019  and  1020 ;  this  would  make  E  lie  between  61  x  10'10  and 
1-29  x  10"10;  the  value  of  e  is  well  between  these  limits.  Hence 
we  conclude  that  the  charge  carried  by  any  gaseous  ion  is  equal 

T.  G.  9 


130  DETERMINATION   OF   THE   CHARGE  [67 

to  the  charge  carried  by  the  hydrogen  ion  in  the  electrolysis  of 
solutions. 

This  conclusion  is  also  confirmed  by  the  experiments  of 
Townsend  already  referred  to.  In  these  experiments  the  charges 
on  the  ions  in  air,  hydrogen  and  carbonic  acid  gas  were  directly 
compared  with  E,  and  proved  to  be  equal  to  it  (see  p.  58). 
Starting  with  this  result  we  can  by  direct  experiment  on  gases 
determine  the  value  of  E,  and  then  by  the  aid  of  the  equation 


the  number  of  molecules  in  a  cubic  centimetre  of  the  gas,  and 
hence  the  mass  of  a  molecule  of  the  gas  ;  proceeding  in  this  way 
we  avoid  all  those  assumptions  as  to  the  shape  and  size  of  the 
molecules  of  the  gas,  and  the  nature  of  the  action  which  occurs 
when  two  molecules  come  into  collision,  which  have  to  be  made 
when  the  same  quantities  are  determined  by  means  of  the  Kinetic 
Theory  of  Gases.  The  value  we  have  found  for  E  makes 

Ar=3'9  x  1019. 

67.  The  determinations  of  e  described  above  have  been  made 
•on  ions  produced  by  Rontgen  or  radium  rays.  The  properties  of 
tthe  ions  in  gases  are  the  same,  however,  whether  the  ions  are 
produced  by  Rontgen,  radium,  Lenard,  or  cathode  rays,  or  by  the 
agency  of  ultra-violet  light.  Evidence  in  support  of  this  is 
.afforded  by  the  fact  that  as  we  have  seen  the  velocity  of  the  ions 
in  the  electric  field  is  the  same  in  whichever  of  the  above-men- 
itioned  ways  they  are  produced.  We  shall  see  too  (Chap.  VII.)  that 
ithey  behave  in  exactly  the  same  way  with  respect  to  their  power 
•of  producing  condensation  of  clouds.  We  have  thus  strong  reasons 
for  thinking  that  the  charge  on  the  ion  does  not  depend  upon 
'the  kind  of  radiation  used  to  liberate  the  ion.  I  have  made  some 
direct  experiments  on  this  point,  and  have  made  measurements 
of  the  charge  on  the  negative  ions  produced  by  the  incidence  of 
ultra-violet  light  on  metals  ;  the  method  used  was  the  same  as  in 
the  case  of  the  ions  produced^by  Rontgen  rays,  and  the  result  was 
that  within  the  limits  of  experimental  error  the  charge  on  the 
negative  ion  produced  by  the  action  of  ultra-violet  light  was  the 
same  as  that  on  the  ion  produced  by  Rontgen  rays*. 

The   case  of  the  ions   produced  by  ultra-violet  light  is  in- 
teresting, as  it  is  the  one  in  which  both  the  values  of  e  and  of  e/m 
*  J.  J.  Thomson,  Phil.  Mag.  v.  48,  p.  547,  1899. 


69]  CARRIED   BY   THE    NEGATIVE    ION.  131 

(when  the  pressure  is  low)  have  been  measured  when  the  ions 
are  produced  by  the  same  kind  of  radiation  in  the  two  experi- 
ments. 

68.  As  e  is  the'  same  as  E  the  charge  on  the  hydrogen  ion, 
while  elm  is  about  a  thousand  times  E/M,  where  M  is  the  mass 
of  the  atom  of  hydrogen,  it  follows  that  ra  is  only  about  1/1000 
of  M,  so  that  the  mass  of  the  earner  of  the  negative  charge  is 
only  1/1000  of  that  of  the  atom  of  hydrogen. 

69.  Let  us  no.w  sum  up  the  results  of  the  determinations  of  e 
and  of  e/m  which  have  been  made  for  the  ions  produced  in  gases  by 
radiations  of  different  kinds.     We  have  seen  that  in  all  the  cases 
in  which  e  has  been  determined  it  has  been  found  equal  to  E,  the 
charge  on  a  hydrogen  ion  in  liquid  electrolysis.     The  charge  on  the 
gaseous  ion  does  not,  like  that  on  the  ions  in  liquids,  depend  on 
the  substance  from  which  the  ions  are  produced  ;  thus  in  the  case 
of  the    ions   produced    by   Rontgen    or  analogous    radiation,  the 
charge  on  an  ion  produced  from  oxygen  is  the  same  as  that  on 
one  produced  from  hydrogen,  though  in  liquids  the  charge  on  an 
oxygen  ion  is  twice  that  on  a  hydrogen  one. 

Again,  at  very  low  pressures,  when  the  negative  ion  can 
escape  getting  entangled  with  the  molecules  of  the  gas  by  which 
it  is  surrounded,  the  mass  as  well  as  the  charge  of  the  negative 
ion  is  invariable  and  much  smaller  than  the  mass  of  the  smallest 
portion  of  ordinary  matter,  i.e.  that  of  an  atom  of  hydrogen, 
recognised  in  the  .Kinetic  Theory  of  Gases.  We  shall  call  each 
of  these  small  negative  ions  a  corpuscle,  thus  negative  electri- 
fication when  the  pressure  of  the  gas  is  low  so  that  there  is  only 
a  very  small  quantity  of  ordinary  matter  present,  consists  of  an 
assemblage  of  corpuscles. 

On  the  other  hand  the  positive  ions  are  as  far  as  we  know 
always  associated   with  masses  which   are  comparable   with  th 
masses  of  the  ordinary  atoms  of  the  gas  in  which  they  occur. 

We  are  at  once  led  by  this  result  to  a  view  of  the  nature  of 
electricity  which  in  many  respects  closely  resembles  that  of  the 
old  '  One  Fluid  Theory  of  Electricity.'  The  '  electric  fluid '  corre- 
sponds to  an  assemblage  of  corpuscles,  negative  electrification 
consisting  of  a  collection  of  these  corpuscles :  the  transference  of 
electrification  from  place  to  place  being  a  movement  of  corpuscles 

9—2- 


132  DETERMINATION   OF  THE   CHARGE,   ETC.  [69 

from  the  place  where  there  is  a  gain  of  positive  electrification  to 
the  place  where  there  is  a  gain  of  negative.  Thus  a  positively 
electrified  body  is  one  which  has  been  deprived  of  some  corpuscles. 
These  corpuscles  may  either  remain  free  or  get  attached  to  mole- 
cules of  matter  with  which  they  come  in  contact ;  thus  positive 
electrification  is  always  associated  with  ordinary  matter,  while 
negative  electrification  may  or  may  not  be,  according  as  the 
corpuscles  are  or  are  not  attached  to  molecules  of  ordinary 
matter.  Thus  in  gas  at  very  low  pressures  the  corpuscles  are 
free,  but  in  gases  at  higher  pressures  they  get  attached  to  the 
molecules  of  the  gas  so  that  there  is  not  much  difference  between 
the  effective  masses  of  the  positive  and  negative  ions ;  that  this 
is  the  case  is  indicated  by  the  results  of  the  experiments  we  have 
described  on  the  velocities  of  the  positive  and  negative  ions  in 
the  electric  field,  for  though  the  negative  ion  moves  faster  than 
the  positive,  the  difference  is  not  great.  We  shall  return  to  the 
development  of  this  corpuscular  theory  of  electricity  in  a  later 
chapter. 


CHAPTER    VII. 

ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS. 

70.  ONE  of  the  most  striking  effects  produced  by  ions  is  the 
influence  they  exert  on  the  condensation  of  clouds.  One  instance 
of  this  is  the  discovery  by  R.  von  Helmholtz*  of  the  effect 
of  an  electric  discharge  on  a  high  pressure  steam  jet.  When 
steam  rushes  out  from  a  jet  placed  near  a  pointed  electrode 
connected  with  an  electric  machine  or  an  induction  coil,  a  re- 
markable change  in  the  appearance  of  the  jet  takes  place  when 
electricity  is  escaping  from  the  electrode.  This  can  conveniently 
be  shown  by  throwing  the  shadow  of  the  jet  on  a  screen;  when 
there  is  no  escape  of  electricity  the  jet  is  nearly  transparent  and 
the  shadow  is  very  slight ;  as  soon  however  as  electricity  begins 
to  escape,  the  opacity  of  the  jet  increases  to  a  remarkable  extent, 
the  shadow  becomes  quite  dark  and  distinct,  and  colours  arising 
from  the  diffraction  of  the  light  by  the  small  drops  of  water 
make  their  appearance,  the  jet  sometimes  presenting  a  very 
beautiful  appearance.  For  an  account  of  the  ways  of  arranging 
the  experiments  so  as  to  observe  these  colours  to  the  best  ad- 
vantage and  of  a  method  by  which  the  size  of  the  drops  of  water 
can  be  deduced  from  the  colour  phenomena,  we  must  refer  to  a 
paper  by  Barusf.  This  effect  evidently  shows  that  the  electrifi- 
cation makes  the  steam  condense  into  water  drops. 

In  a  later  paper  by  R.  von  Helmholtz  and  RicharzJ;,  published 
after  the  death  of  the  former,  the  authors  show  that  a  steam  jet 
is  affected  by  making  or  breaking  the  current  through  the  primary 

*  R.  v.  Helmholtz,  Wied.  Ann.  xxxii.  p.  1,  1887 ;  see  also  Bidwell,  Phil.  Mag. 
v.  29,  p.  158,  1890. 

t  Barus,  American  Journal  of  Meteorology,  ix.  p.  488,  1893. 
£  R.  v.  Helmholtz  and  Richarz,  Wied.  Ann.  xl.  p.  161,  1890. 


134         ON   SOME   PHYSICAL  PROPERTIES   OF   GASEOUS   IONS.          [70 

of  an  induction  coil,  even  when  the  terminals  of  the  secondary 
placed  in  the  neighbourhood  of  the  jet  are  separated  by  much 
more  than  the  sparking  distance,  and  that  the  effects  persist 
even  when  the  terminals  are  wrapped  in  moist  filter-paper  so 
as  to  catch  any  metallic  particles  that  might  be  given  off  from 
them. 

R.  vori  Helmholtz  and  Richarz  (loc.  cit)  showed  that  the 
steam  jet  was  affected  by  gases  from  the  neighbourhood  of  flames 
whether  these  were  luminous  or  not ;  the  very  cool  flames  of 
burning  ether  and  alcohol  are  exceptions  to  this  statement. 

A  platinum  wire  raised  to  a  dull  red  heat  affected  the  jet 
when  electrified,  and  if  raised  to  a  bright  yellow  heat  affected 
the  jet  even  when  unelectrified,  except  when  the  wire  was  sur- 
rounded by  hydrogen,  in  which  case  the  unelectrified  wire  had 
no  effect.  Coal  gas  passed  through  platinum  gauze  raised  to 
a  dull  red  heat  also  influenced  the  jet. 

The  jet  is  also  affected  by  the  presence  in  its  neighbourhood 
of  certain  substances  such  as  sulphuric  acid,  also  by  gases  which 
are  dissociating  or  undergoing  chemical  changes  in  the  air  such 
as  N2O4  or  N02,  it  is  not  affected  by  ozone  or  hydrogen  peroxide. 
If  however  ozone  is  destroyed  by  bubbling  through  such  sub- 
stances as  solutions  of  potassium  iodide  or  potassium  perman- 
ganate, the  gas  which  emerges  has  the  power  of  affecting  the  jet; 
this  gas  has  also  the  power  of  forming  clouds  when  it  comes 
into  contact  with  moist  air,  as  was  first  shown  by  Meissner*; 
experiments  on  this  point  have  also  been  made  by  R.  von  Helm- 
holtz and  Richarz  and  by  J.  S.  Townsendf.  The  action  in  this 
case  and  in  other  cases  of  the  effect  of  chemicals  ie,  as  we  shall 
see,  probably  due  to  the  formation  of  some  substance  which 
dissolves  in  the  drops  of  water  arid  lowers  their  vapour  pressure ; 
thus  the  drops  in  this  case  are  not  formed  of  pure  water,  but  of 
more  or  less  dilute  solutions. 

Moist  air  drawn  over  phosphorus,  sodium  or  potassium  also 
affects  the  jet. 

Lenard  and  Wolff  J  also  showed  that  the  incidence  of  ultra- 

*  Meissner,  Jahresber.  f.  Chemie,  1863,  p.  126. 

t  J.  S.  Townsend,  Proc.  Camb.  Phil,  Soc.  x.  p.  52,  1898. 

+  Lenard  and  Wolff,  Wied.  Ann.  xxxvii.  p.  443,  1899. 


70]          ON  SOME  PHYSICAL  PROPERTIES  OF  GASEOUS  IONS.         135 

violet  light  on  a  zinc  plate  or  on  some  fluorescent  solutions  in  the 
neighbourhood  of  a  steam  jet  produced  condensation  in  the  jet; 
a  similar  effect  was  produced  by  ultra-violet  light  passing  through 
quartz.  Richarz*  showed  that  the  incidence  of  Rontgen  rays 
produced  condensation  in  the  jet.  There  was  for  some  time  con- 
siderable difference  of  opinion  as  to  the  cause  of  this  behaviour 
of  the  steam  jet ;  the  earliest  researches  on  this  subject  came 
at  a  time  when  the  experiments  of  Aitkenf,  of  CoulierJ  and  of 
Kiessling§  had  drawn  attention  to  the  great  effect  produced  by 
dust  on  cloudy  condensation.  These  physicists  had  shown  that 
the  clouds  produced  by  the  lowering  of  temperature  resulting 
from  a  small  adiabatic  expansion  of  the  damp  dusty  air  of  an 
ordinary  room  entirely  disappeared  if  the  dust  were  filtered  out 
of  the  air :  the  drops  in  the  cloud  were  shown  to  collect  round 
the  particles  of  dust,  the  water  drops  were  thus  able  to  start  with 
a  finite  radius — that  of  the  dust  particle — and  so  had  not  to 
pass  through  the  stage  when  their  radius  was  of  molecular 
dimensions,  when,  as  Lord  Kelvin  has  shown,  the  effect  of  surface 
tension  would  lead  to  such  intense  evaporation  as  soon  to  cause 
the  disappearance  of  the  drops. 

The  discovery  of  the  effect  of  dust  on  the  condensation  of 
water  vapour  produced  a  tendency  to  ascribe  the  formation  of 
clouds  in  all  cases  to  dust  and  to  dust  alone ;  in  fact,  to  use  the 
indication  of  the  steam  jet  as  a  measure  of  the  dustiness  of  the 
air;  thus,  for  example,  Lenard  and  Wolff  ascribed  the  effect 
which  they  found  was  produced  by  the  incidence  of  ultra-violet 
light  on  metals  to  metallic  dust  given  off  by  the  metal  under 
the  influence  of  the  light.  On  the  other  hand,  R.  von  Helmholtz,. 
and  later  Richarz,  strongly  maintained  the  view  that  many  of  the 
effects  they  observed  were  not  due  to  dust,  but  to  ions,  and] 
they  gave  strong  arguments  and  made  some  striking  experi- 
ments in  support  of  this  view ;  as  however  this  evidence  ~s 
somewhat  indirect,  and  as  the  truth  of  their  view  has  been 
indisputably  proved  by  the  direct  experiments  recently  made  by 

*  Richarz,  Wied.  Ann.  lix.  p.  592,  1896. 

t  Aitken,  Nature,  xxiii.  pp.  195,  384,   1880.     Trans.  Roy.  Soc.  Edin. 
p.  337,  1881. 

£  Coulier,  Journal  de  Pharm.  et  de  Chemie,  xxii.  p.  165,  1875. 
§  Kiessling,  Naturw.  Verein  Hamburg -Altona,  viii.  1,  1884. 


136 


ON    SOME   PHYSICAL   PROPERTIES   OF   GASEOUS    IONS. 


[71 


C.  T.  R.  Wilson*,  we  shall  proceed  at  once  to  a  description  of 
his  researches. 

71.  The  method  used  by  Wilson  was  to  suddenly  cool  the 
moist  gas  by  an  adiabatic  expansion,  so  that  the  gas  which  was 
saturated  with  water  vapour  before  cooling  became  supersaturated 
afterwards.  One  of  the  arrangements  used  by  Wilsoo  to  produce 


ToPump 


Fig.  37. 

the  expansion  is  shown  in  Fig.  37  :  the  way  in  which  the  appa- 
ratus works  has  already  been  explained  (see  p.  125).  It  is  very 
important  in  these  experiments  that  the  expansions  which  produce 
the  cloud  should  be  as  rapid  as  possible,  for  with  slow  expansions 

*  C.  T.  E.  Wilson,  Phil.  Trans.  189,  p.  265,  1897. 


72] 


ON    SOME   PHYSICAL    PROPERTIES   OF   GASEOUS   IONS. 


137 


as  soon  as  the  supersaturation  is  sufficient  for  the  first  drops  to 
be  formed,  if  these  have  time  to  grow  before  the  expansion  is 
completed,  they  will  rob  the  air  of  its  moisture,  and  the  super- 
saturation  will  not  rise  much  above  the  value  required  for  the 
formation  of  the  first  drops.  To  ensure  this  rapid  expansion, 
the  piston  P,  Fig.  37,  should  be  light  and  able  to  move  freely 
up  and  down,  and  the  arrangement  by  which  the  difference  of 
pressure  between  the  inside  and  outside  of  the  cylinder  is  pro- 
duced should  work  very  rapidly. 

72.  Using  an  arrangement  of  this  nature,  Wilson  found  that 
when  dusty  air  filled  the  expansion  chamber  a  very  slight  expan- 
sion was  sufficient  to  produce  a  dense  fog;  if  this  was  allowed  to 
settle  and  the  process  repeated,  the  air  by  degrees  got  deprived  of 
the  dust  which  was  carried  down  by  the  fog;  when  the  air  became 
dust-free  no  fogs  were  produced  by  small  expansions.  If  we 
take  as  the  measure  of  the  expansion  the  ratio  of  the  final  to 
the  initial  volume  of  the  gas,  no  cloud  was  produced  in  the  dust- 
free  air  until  the  expansion  was  equal  to  1'25.  When  the  ex- 
pansion was  between  1'25  and  1P38,  a  few  drops  made  their  ap- 
pearance ;  these  drops  were  very  much  fewer  in  hydrogen  than  in 
air.  On  increasing  the  expansion  beyond  1'38  a  much  denser 
cloud  was  produced  in  the  dust-free  gas,  and  the  density  of  the 
cloud  now  increased  very  rapidly  with  the  expansion.  Thus  we 
see  that  even  when  there  is  no  dust,  cloudy  condensation  can  be 
produced  by  sudden  expansions  if  these  exceed  a  certain  limit. 
This  limit  appears  to  be  independent  of  the  nature  of  the  gas, 
as  is  shown  by  the  following  table,  which  gives  the  ratio  of  the 


Rain-like  condensation           Cloud-like  condensation 

Gas 

Final  /initial  i       Super- 
volume        •    saturation  i 

Final  /  initial 
volume 

Super- 
saturation 

Air    .    . 

1-252 

4-2 

1-375 

7-9 

Oxygen  

1-257 

4-3 

1-375      . 

7-9 

Nitrogen    

1-262 

4-4 

1-375 

7-9 

Hydrogen  

— 

1-375 

7-9 

Carbonic  acid 

1-365 

4-2 

1-53 

7-3 

Chlorine    

1-30 

3-4 

1-44 

5-9 

volumes  required  to  produce  the  first  or  rain-like  stage  of  con- 
densation and  the  supersaturation,  i.e.  the  ratio  of  the  pressure 


138          ON   SOME    PHYSICAL    PROPERTIES   OF   GASEOUS   IONS.  [73 

of  the  aqueous  vapour  actually  present  when  the  condensation 
begins  to  the  saturation  vapour  pressure  at  that  temperature : 
the  third  and  fourth  columns  give  the  corresponding  quantities 
for  the  second  stage  of  the  condensation,  i.e.  when  the  expansion 
produces  a  dense  cloud. 

The  rain-like  condensation  is  absent  in  hydrogen. 

73.  The  description  given  above  relates  to  the  behaviour  of  gas 
in  the  normal  state ;  on  exposing  the  gas  to  Rontgen  rays,  Wilson 
found  that  as  in  the  normal  gas,  there  were  no  drops  until  the 
expansion  was  equal  to  1*25  ;  on  passing  this  limit  however  the 
density  of  the  cloud  was  very  greatly  increased  by  the  rays,  and 
if  these  were  strong  the  few  drops  which  were  all  that  were  formed 
when  the  rays  were  absent  were  replaced  by  a  dense  and  almost 
opaque  cloud.    The  strength  of  the  rays  does  not  affect  the  expan- 
sion required  to  produce  the  cloud;  no  matter  how  strong  the  rays 
may  be  there  is  no  cloud  produced  unless  the  expansion  exceeds 
T25  :  the  strength  of  the  rays  increases  the  number  of  drops  in 
the  cloud,  but  does  not  affect  the  stage  at  which  the  cloud  begins. 
The  effect  of  the  rays  in  producing  a  cloud  lasts  some  few  seconds 
after  the  rays  have  been  cut  off.     Wilson*  has  shown  that  the 
radiation   from   uranium   and  other  radio-active  substances  pro- 
duces the  same  effect  as  Rontgen  rays,  as  does  also  ultra-violet 
light  when  incident  upon  such  a  metal  as  zinc :  the  effects  pro- 
duced by  ultra-violet  light  are  however  somewhafc  complicated  and 
we  shall  have  to  return  to  them  again. 

74.  That  the  effect  produced  by  Rontgen  and  uranium  rays  is 
due  to  the  production  of  charged  ions  produced  in  the  gas  can  be 
shown  directly  by  the  following  experiment.     If  the  ions  produced 
by  the  Rontgen  rays  act  as  nuclei  for  the  water  drops,  then  since 
these  ions  can  be  withdrawn  from  the  gas  by  applying  to  it  a 
strong  electric  field,  it  follows  that  a  cloud  ought  not  to  be  formed 
by  the  rays  when  the  air  which  is  expanded  is  exposed  to  a  strong 
electric  field  while  the  rays  are  passing  through   it.     This  was 
found  to  be  the  case,  and  the  experiment  is  a  very  striking  one. 
Two  parallel  plates  were  placed  in  the  vessel  containing  the  dust- 
free  air :   these  plates  were  about   5  cm.  apart,  and   were  large 
enough  to  include  the  greater  part  of  the  air  between  themf.    The 

*  C.  T.  E.  Wilson,  Phil.  Tram.  192,  p.  403,  1899. 
t  J.  J.  Thomson,  Phil.  Mag.  v.  46,  p.  528,  1898. 


76]  ON    SOME   PHYSICAL   PROPERTIES   OF  GASEOUS   IONS.          139 

plates  could  be  connected  with  the  terminals  of  a  battery  of  small 
storage  cells  giving  a  potential  difference  of  about  400  volts. 
Rontgen  rays  passed  through  the  gas  between  the  plates ;  the  gas 
had  previously  been  freed  from  dust.  When  the  plates  were  dis- 
connected from  the  battery  a  suitable  expansion  produced  a  dense 
cloud ;  when  however  the  plates  were  connected  with  the  battery 
only  a  very  light  cloud  was  produced  by  the  expansion,  and  this 
cloud  was  almost  as  dense  when  the  Rontgen  rays  did  not  pass 
through  the  air  as  when  they  did. 

75.  When  a  dense  cloud  has  been  produced  by  Rontgen  rays 
by  an  expansion  between  1-25  and  1'38,  or  by  an  expansion  with- 
out Rontgen  rays  greater  than  1*38,  then  for  some  little  time  after 
drops  can  be  produced  by  expansions  less  than  1*25,  and  these  are 
not  eliminated   by  the  action  of  an  electric  field.     A  dense  fog 
apparently  leaves  behind  it  little  drops  of  water,  which,  though 
too  minute  to  be  visible,  act   in    the  same  way  as  particles  of 
dust,  producing  cloudy  condensation  with  very  slight  expansions. 
Wilson*  has  also  shown  that  when  electricity  is  discharged  from  a 
pointed  electrode  in  the  expansion  chamber,  cloudy  condensation 
is,  as  in  the  case  of  exposure  to  Rontgen  rays,  much  increased  for 
expansions  between  1'25  and  1*38.   When  the  discharge  was  stopped 
before  the  expansion  took  place,  it  was  found  that  fogs  could  be 
produced  for  1  or  2  minutes  after  the  cessation  of  the  discharge ; 
the  expansion   required   to  produce   the    fog   diminished    as  the 
interval  after  the  cessation  of  the  discharge  increased,  showing 
that  some  of  the  nuclei  produced  had  grown  during  this  interval. 
This  effect   is  probably  due  to  the  formation  of  some  chemical 
compound  during  the  discharge,  perhaps  nitric  acid,  which  by  dis- 
solving in  the  drops  lowers  their  vapour  pressure. 

76.  Wilson  (loc.  cit.)  showed  that  the  passage  of  ultra-violet 
light  through  a  gas  (as  distinct  from  the  effects  produced  when  it 
is  incident  on  a  metallic  surface)  produces  very  interesting  effects 
on  the  condensation  of  clouds.     If  the  intensity  of  the  light  is 
small,  then  no  clouds  are  produced  unless  the  expansion  equals 
that  (1'25)  required  to  produce  clouds  in  gases  exposed  to  Rontgen 
rays.     If  however  the  ultra-violet  light  is  very  intense,  clouds  are 
produced  in  air  or  in  pure  oxygen,  but  not  in  hydrogen,  by  very 

*  C.  T.  R.  Wilson,  Phil.  Tram.  192,  p.  403,  1899. 


140          ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS    IONS.  [77 

much  smaller  expansions,  and  the  expansion  required  decreases  as 
the  time  of  exposure  to  the  light  increases ;  thus  the  nuclei  pro- 
ducing the  clouds  grow  under  the  influence  of  the  light.  If  the 
light  is  exceedingly  strong,  clouds  are  produced  in  air  or  oxygen 
without  any  expansion  at  all;  these  clouds  are. exceedingly  fine 
and  may  last  for  hours  after  the  light  is  cut  off.  Wilson  was  even 
able  to  produce  these  clouds  in  air  standing  over  a  17°/0  solution  of 
caustic  potash,  and  which  therefore  was  not  saturated  with  water 
vapour;  in  this  case  the  drops  lasted  for  three  hours  after  the 
light  was  cut  off,  so  that  there  could  be  very  little  evaporation 
from  the  drops ;  this,  as  Wilson  points  out,  shows  that  the  drops 
cannot  be  pure  water.  These  clouds  are  probably  analogous  to 
those  observed  many  years  ago  by  Tyndall*,  when  ultra-violet 
light  passes  through  air  containing  the  vapours  of  certain  sub- 
stances of  which  amyl-nitrite  was  the  one  which  gave  the  most 
striking  effects.  The  effects  can  be  explained  by  the  formation 
under  the  influence  of  the  ultra-violet  light  of  some  substance — 
Wilson  suggests  that  in  his  experiments  it  was  H202 — which  by 
dissolving  in  the  drops  as  they  form  lowers  the  equilibrium  vapour 
pressure,  and  thus  enables  the  drops  to  grow  under  circumstances 
which  would  make  drops  of  pure  water  evaporate.  This  explana- 
tion is  supported  by  the  fact  that  ultra-violet  light  does  not  pro- 
duce these  clouds  in  water  vapour  by  itself  or  in  hydrogen :  and 
also  by  the  fact  that,  unlike  the  clouds  due  to  Rontgen  rays,  these 
clouds  formed  by  ultra-violet  light  do  not  diminish  in  density  when 
a  strong  electric  field  is  applied  to  the  gas,  showing  that  the  nuclei 
are  either  not  charged  or  that  if  they  are  charged  they  are  so 
loaded  with  foreign  molecules  that  they  do  not  move  perceptibly 
in  the  electric  field. 

77.  Buisson  f,  who  examined  this  question  with  great  care,  could 
not  detect  any  conductivity  in  the  air  through  which  the  ultra-violet 
light  passed.  Lenardj  has  however  shown  recently  that  a  certain 
kind  of  ultra-violet  light  which  is  absorbed  so  quickly  by  the  air 
as  to  be  extinguished  within  a  space  of  a  few  centimetres  when  the 
air  is  at  atmospheric  pressure,  does  produce  electrical  conductivity 

*  J.  Tyndall,  Phil.  Trans.  160,  p.  333,  1870. 

f  Buisson  quoted  by  Perrin,  Theses  presentees  a  la  Faculte  des  Sciences  de  Paris, 
1897,  p.  31. 

J  Lenard,  Drude's  Annalen,  i.  p.  486 ;  iii.  p.  298,  1900. 


78]  ON   SOME   PHYSICAL    PROPERTIES   OF   GASEOUS    IONS.          141 

'•if 

in  the  gas  through  which  it  passes,  and  that  a  charged  conductor 
placed  in  the  neighbourhood  of  air  traversed  by  these  rays  loses  its 
charge,  and  does  so  much  more  rapidly  when  the  charge  is  positive 
than  when  it  is  negative.  Lenard  determined  the  velocity  of  the 
negative  ions  by  a  method  analogous  to  that  described  on  page  38 
and  found  for  this  velocity  through  air  at  atmospheric  pressure 
3*13  cm./sec.  under  a  potential  gradient  of  a  volt  per  cm.:  this  is 
about  twice  the  velocity  of  the  ions  produced  by  Rontgen  rays: 
on  the  other  hand  the  velocity  of  the  positive  ions  under  the  same 
potential  gradient  was  not  more  than  "0015  cm./sec.,  which  is  only 
about  one  thousandth  part  of  the  velocity  of  the  positive  ion  pro- 
duced by  Rontgen  rays.  The  greater  mobility  of  the  negative 
ions  explains  why  the  leak  from  a  positively  charged  body  in  the 
neighbourhood  of  the  ionised  gas  is  so  much  more  rapid  than 
that  from  a  negatively  charged  one.  We  shall  return  to  this  point 
in  the  chapter  on  the  effect  of  ultra-violet  light  on  gases. 

78.  The  results  obtained  by  Wilson  and  Lenard  seem  to  point 
to  the  conclusion  that  when  gas  is  exposed  to  the  action  of  ordinary 
ultra-violet  light,  we  have  some  chemical  action  taking  place 
which  results  in  the  formation  of  a  product  which  by  dissolving 
in  water  lowers  the  vapour  pressure  over  the  drops  and  thus 
facilitates  their  formation.  Whenjthese  drops  are  exposed  to  the 
influence  of  ultra-violet  light  of  the  kind  investigated  by  Lenard, 
they  lose,  as  so  many  other  bodies  do  when  illuminated  by  light 
of  this  kind,  negative  electricity,  and  it  is  the  negative  ions 
liberated  in  this  way  which  produce  the  electrical  conductivity 
investigated  by  Lenard.  The  difference  between  the  action  of 
ultra-violet  light  and  Rontgen  rays  is  that  the  former  when  very 
intense  can  produce  clouds  with  little  or  no  expansion,  while  the 
latter  cannot ;  this  on  the  theory  given  above  is  due  to  ultra- 
violet light  being  more  efficient  than  Rontgen  rays  in  promoting 
chemical  action ;  there  are  many  examples  of  this,  e.g.  the  com 
bination  of  hydrogen  and  chlorine. 

The  influence  of  minute  traces  of  soluble  substances  in  pro- 
moting the  formation  of  clouds  has  been  shown  in  a  very  straight- 
forward way  in  some  experiments  made  by  H.  A.  Wilson*.  The 
writerf  has  shown  how  drops,  even  if  their  existence  is  very 

*  H.  A.  Wilson,  Phil.  Mag.  v.  45,  p.  454,  1898. 

t  J.  J.  Thomson,  Phil.  Mag.  v.  36,  p.  313,  1893 ;  B.  A.  Report,  1894. 


142         ON   SOME   PHYSICAL   PROPERTIES  OF  GASEOUS  IONS.          [79 

transient,  would  facilitate  the  progress  of  chemical  combination 
between  the  gases  surrounding  them,  and  how  this  action  would 
afford  an  explanation  of  the  remarkable  fact  investigated  by 
Baker*  and  Pringsheimf,  that  the  occurrence  of  some  of  the  best 
known  cases  of  chemical  combination  between  gases  depends  upon 
the  presence  of  moisture  and  does  not  take  place  in  gases  dried 
with  extreme  care. 

79.  Nuclei  from  metals.  C.  T.  R.  Wilson  J  has  shown  that 
certain  metals  produce  nuclei  which  cause  cloudy  condensation 
when  the  expansion  exceeds  T25,  although  the  effects  are  much 
more  marked  when  the  expansion  is  increased  to  1'30.  The  amount 
of  this  effect  depends  greatly  upon  the  kind  of  metal  used :  amal- 
gamated zinc  gives  comparatively  dense  clouds,  polished  zinc  and 
lead  also  show  the  effect  well ;  on  the  other  hand  polished  copper 
and  tin  produce  no  appreciable  effect.  The  order  of  the  metals 
in  respect  to  their  power  of  producing  nuclei  for  cloudy  condensa- 
tion is  the  same  as  their  order  in  respect  to  their  power  of 
affecting  a  photographic  plate  placed  at  a  small  distance  from  their 
surface,  a  subject  which  has  been  studied  by  Russell§  and  ColsonjL 
The  effect  produced  by  the  presence  of  a  metal  on  clouds  in 
hydrogen  is  very  slight. 

Although  the  expansion  required  to  produce  cloudy  condensa- 
tion when  metals  are  present  is  the  same  as  when  charged  ions 
are  produced  by  Rontgen  rays,  the  metal  effect  differs  from  the 
Rontgeii  ray  effect  inasmuch  as  it  is  not  diminished  by  the  appli- 
cation of  an  intense  electric  field.  It  is  possible  however  that  in 
still  air  the  ionised  gas  is  confined  to  a  layer  close  to  the  surface 
of  the  metal,  and  that  the  rush  of  gas  caused  by  the  sudden 
expansion  detaches  the  layer  and  scatters  the  ions  throughout  the 
volume  of  the  gas.  If  this  be  the  case,  then,  since  the  ions  are 
only  free  during  the  short  time  the  expansion  is  taking  place,  they 
will  not  be  appreciably  affected  by  the  electric  field,  which  cannot 
in  the  short  time  at  its  disposal  sweep  the  ions  from  the  gas. 
The  existence  of  such  a  layer  of  ionised  gas  next  the  metal  is 

*  Baker,  Phil.  Tram.  179,  p.  571,  1888. 

t  Pringsheim,  Wied.  Ann.  xxxii.  p.  384,  1887. 

J  C.  T.  R.  Wilson,  Phil.  Trans.  192,  p.  403,  1899. 

§  Russell,  Proc.  Eoy.  Soc.  Ixi.  p.  424,  1897  ;  Ixiii.  p.  102,  1898. 

||  Colson,  Comptes  Rendus,  123,  p.  49,  1896. 


79]  ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          143 

,» 

rendered  very  probable  by  the  effects  which  are  known  to 
accompany  the  splashing  of  drops  of  water,  mercury  and  many 
other  liquids.  Thus  Lenard*  showed  that  when  drops  of  water 
splashed  against  a  metal  plate,  the  drops  of  water  became  posi- 
tively electrified  while  there  was  negative  electrification  in  the 
surrounding  air.  Air  shaken  up  in  a  bottle  containing  mercury 
becomes  negatively  electrified.  Lord  Kelvin  f  has  shown  that  when 
air  is  bubbled  through  water  it  comes  off  charged  with  negative 
electricity.  I  have  recently  found  that  if  the  air  is  made  to 
bubble  with  great  vigour  through  water,  then  when  it  leaves  the 
water  it  contains  positive  as  well  as  negative  ions,  though  the 
latter  are  the  more  numerous  ;  air  treated  in  this  way  was  found  to 
discharge  a  body  with  a  negative  charge,  though  not  so  rapidly  as 
one  with  a  positive  one.  As  another  illustration  of  electrification 
produced  by  an  agitation  at  the  surface  of  water  we  may  mention 
that  Holmgren |  has  shown  that  when  two  wet  cloths  are  brought 
together  and  then  pulled  suddenl^  apart  electrification  is  pro- 
duced, the  positive  electrification  being  on  the  cloth,  the  negative 
in  the  air.  He  also  found  that  when  the  area  of  a  water  surface 
was  changing  rapidly,  as  for  example  when  ripples  were  travelling 
over  the  surface,  electrification  was  produced,  the  positive  elec- 
tricity being  on  the  water  and  the  negative  in  the  air.  The  writer 
found  §  that  when  the  liquids  were  surrounded  by  pure  hydrogen 
instead  of  air,  the  electrification  produced  by  splashing  was 
exceedingly  small :  Wilson,  as  has  already  been  stated,  found  that 
the  effect  produced  by  metals  on  cloudy  condensation  was  exceed- 
ingly small  in  hydrogen.  These  facts  are  sufficient  to  show  that 
a  disturbance  at  the  surface  of  a  large  number  of  substances  is 
accompanied  by  the  spread  of  ions  through  the  adjoining  gas : 
the  most  natural  explanation  of  this  fact  is  that  there  is  on  the 
surface  of  these  bodies  a  thin  layer  of  ionised  gas  which  can  be 
detached  by  mechanical  agitation.  It  is  important  to  notice  that 
if  this  layer  of  ionised  gas  were  very  close  to  the  surface  of  the 
metal,  the  ions  in  it  would  not  be  dispersed  into  the  surrounding- 
gas  even  though  the  metal  were  charged  up  so  as  to  produce  an 

*  Lenard,  Wied.  Ann.  xlvi.  p.  584,  1892. 
t  Lord  Kelvin,  Proc.  Roy.  Soc.  Ivii.  p.  335,  1894. 

t  Holmgren,  Sur  le  Developpement  de  VelectriciiS  au  contact  de  I'air  et  de  Veau. 
Societe  physiographique  de  Lond.  1894. 

§  J.  J.  Thomson,  Phil.  Mag.  v.  37,  p.  341,  1894. 


144         ON   SOME   PHYSICAL   PROPERTIES   OF  GASEOUS   IONS.          [80 

electric  field  of  very  considerable  strength.  For  suppose  we  have 
a  charge  e  at  a  point  P  at  a  distance  r  from  a  plane  conducting 
surface,  then  there  will,  in  consequence  of  the  electricity  of 
opposite  sign  induced  on  the  plane,  be  a  pull  on  the  charge  at  P 
towards  the  plane  equal  to  e2/4r2 ;  if  there  is  an  external  field  of 
strength  F  tending  to  make  the  charged  body  move  away  from 
the  plane,  this  will  not  be  able  to  overcome  the  attraction  towards 
the  plane  unless  Fe  is  greater  than  e2/4r2,  or  F  greater  than  e/4r2. 
Let  us  suppose  e  is  equal  to  the  charge  on  an  ion,  3'4  x  10~10  in 
electrostatic  units,  and  that  the  strength  of  the  electric  field  is 
100  volts  per  centimetre  which  on  the  electrostatic  system  is 
equal  to  J,  then  we  see  that  the  force  on  the  ion  in  this  strong 
field  will  be  towards  the  plate,  i.e.  the  ion  will  not  be  driven  into 
the  surrounding  gas  if  r  is  less  than  1'G  x  10~5 ;  we  see  from  this 
example  that  it  must  be  exceedingly  difficult  to  detach  very  thin 
layers  of  ionised  gases  by  electrical  means. 

80.  The  few  nuclei  that  produce  rain-like  condensation  with 
expansions  between  1*25  and  1*38  in  gases  not  exposed  to  any 
external  ionising  agent  may  possibly  I  think  come  from  a  layer  of 
gas  torn  off  the  water  in  the  vessel  by  the  disturbance  caused  by 
the  expansion.  These  nuclei,  as  Wilson  has  shown,  are  not  removed 
by  an  electric  field,  and  yet  they  produce  clouds  with  exactly  the 
same  expansions  as  is  required  for  the  charged  ions  produced  by 
Rontgen  rays.  We  have  seen  (see  Chap.  I.)  that  even  in  gases  in 
the  normal  state  there  is  a  small  amount  of  conductivity,  indicat- 
ing the  presence  of  a  few  free  ions,  and  these  alone  would  cause 
the  formation  of  a  few  drops,  but  if  these  were  the  nuclei  mainly 
responsible  for  the  rain-like  condensation  they  ought  to  be 
removed  by  the  electric  field ;  indeed  it  seems  not  impossible  that 
some  of  the  nuclei  which  produce  the  electrical  conductivity  in 
normal  air  may  have  diffused  from  the  layers  of  ionised  gas  at  the 
surface  of  liquids  or  solids  in  contact  with  the  gas.  If,  as  Elster 
and  Geitel  hold,  the  gradual  increase  in  the  rate  of  escape  of  the 
electricity  which  occurs  after  fresh  gas  is  brought  into  a  closed 
vessel  is  not  due  to  the  settling  down  of  dust  from  the  gas,  then 
this  phenomenon  is  an  additional  argument  in  favour  of  the  view 
that  layers  of  ionised  gas  next  the  surface  of  solids  or  liquids 
exert  a  considerable  influence  on  the  condensation  of  clouds  by 
expansion.  The  effect  could  be  easily  explained  as  due  to  the  slow 


81]  ON    SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          145 

diffusion  of  ionised  gas  from  the  walls  of  the  vessel  in  which  the 
gas  is  contained. 

Comparative  efficiency  of  positive  and  negative  ions  in  producing 
condensation  of  clouds. 

81.  The  writer*  in  1893  made  an  experiment  with  a  steam  jet 
which  showed  that  negative  electrification  had  a  decidedly  greater 
effect  in  promoting  condensation  than  positive.  The  following 
arrangement  was  used.  A  vertical  glass  tube  dipped  into  the  steam 
chamber,  and  to  the  top  of  this  tube  was  fused  a  horizontal  cross 
piece,  the  steam  issued  from  nozzles  at  the  ends  of  the  cross 
piece ;  into  these  nozzles  pointed  platinum  wires  were  fused,  and 
these  wires  were  connected  with  the  terminals  of  a  small  induction 
coil.  When  the  coil  was  in  action  there  was  great  condensation  in 
the  two  jets,  but  the  jet  at  the  nozzle  connected  with  the  negative 
terminal  of  the  coil  was  always  denser  than  that  connected  with 
the  positive ;  this  was  not  due  to  any  want  of  symmetry  in  the 
tubes  or  differences  in  the  nozzles,  for  on  reversing  the  coil  the 
denser  cloud  passed  from  one  nozzle  to  the  other.  No  sparks 
passed  between  the  platinum  electrodes,  the  strength  of  the  coil 
being  only  sufficient  to  give  a  non-luminous  discharge  from  their 
points. 

Later  in  1898f  1  observed  indications  of  a  similar  effect  when 
clouds  were  produced  by  expansion,  but  the  subject  was  first 
systematically  investigated  by  C.  T.  R.  Wilson  J  in  1899.  Wilson 
investigated  the  amount  of  expansion  required  to  make  positive 
and  negative  ions  act  as  nuclei  for  the  condensation  of  water 
drops ;  he  used  several  methods,  the  arrangement  of  the  apparatus 
in  one  of  these  is  shown  in  Fig.  38.  The  vessel  in  which  the 
clouds  were  observed  was  nearly  spherical  and  about  5'8  cm.  in 
diameter.  It  was  divided  into  two  equal  chambers  by  a  brass 
partition  (about  1  mm.  thick)  in  the  equatorial  plane ;  the  vessel 
was  cut  in  two  and  the  edges  of  the  two  halves  ground  smooth,  to 
allow  them  to  be  easily  cemented  against  the  face  of  the  partition. 
The  latter  was  circular  and  had  a  narrow  strip  of  brass  soldered 
to  each  face  extending  all  round  the  circumference  exc£Jfl*for  a 

*  J.  J.  Thomson,  Phil.  Mag.  v.  36,  p.  313,  1893. 

t  J.  J.  Thomson,  Phil.  Mag.  v.  46,  p.  528,  1898. 

£  C.  T.  R.  Wilson,  Phil.  Tram.  193,  p.  289,  1899. 

T.  G.  10 


146 


ON  SOME   PHYSICAL  PROPERTIES  OF   GASEOUS   IONS. 


[81 


gap  at  the  top.    When  the  halves  of  the  glass  vessel  were  cemented 
against  these  strips,  a  slit  was  left  at  the  gap  about  4 '5  cms.  long 


Fig.  38. 

and  2'5  mm.  wide  on  each  side  of  the  partition.  This  slit  was 
covered  with  a  thin  piece  of  aluminium  cemented  to  the  outer 
surface  of  the  glass  and  to  the  edge  of  the  brass  partition.  A 
thin  layer  of  air  in  contact  with  each  surface  of  the  partition 
could  thus  be  exposed  to  Rontgen  rays  from  a  source  vertically 
over  the  dividing  plate.  Each  half  of  the  apparatus  contained  a 
second  brass  plate  parallel  to  the  central  plate  and  1*8  cm.  from 
it.  There  was  room  between  the  sides  of  these  plates  and  the 
walls  of  the  vessel  for  the  air  to  escape  when  the  expansion  was 
made.  To  keep  the  beam  of  Rontgen  rays  parallel  to  the  surface 
of  the  partition  a  lead  screen  with  a  slit  4  mm.  wide  was  placed 
about  2  cm.  above  the  aluminium  window  of  the  glass  vessel  : 
this  screen  was  moved  until  when  both  plates  were  kept  at  the 
same  potential  exactly  equal  fogs  were  obtained  on  the  two  sides. 
The  metal  plates  were  covered  with  wet  filter-paper  to  get  rid 
of  any  ions  due  to  the  metal.  Suppose  now  that  the  middle 
plate  is  earthed  while  the  left-hand  plate  is  at  a  lower  and 
the  right-hand  plate  at  a  higher  potential.  Then  it  is  evident 
since  the  ionisation  is  confined  to  a  layer  close  to  the  middle  plate 
thatflMfcler  these  circumstances  the  left  half  of  the  vessel  will 
contain  positive  ions  and  the  right  half  negative  ones.  Wilson 
found  that  with  an  expansion  of  T28  there  was  a  dense  fog  in  the 
half  containing  the  negative  ions,  and  only  a  few  drops  in  the 


81] 


ON   SOME   PHYSICAL   PROPERTIES    OF   GASEOUS   IONS.          147 


half  containing  the  positive  ones,  and  that  this  excess  of  con- 
densation in  the  negative  half  continued  until  the  expansion  was 
equal  to  1'31,  when  little  or  no  difference  was  to  be  seen  in  the 
clouds  in  the  two  halves.  Care  was  taken  that  the  potential  of 
the  positive  plate  should  exceed  that  of  the  middle  one  by  the 
same  amount  as  this  exceeded  the  potential  of  the  negative 
plate. 

The  difference  between  the  effects  produced  by  positive  and 
negative  ions  is  shown  in  the  following  table,  where  the  time  of 
fall  of  the  drops  is  used  to  measure  the  number  of  nuclei  which 
produce  condensation ;  if  this  number  is  small,  then  the  water 
drops  formed  round  them  will  be  large  and  will  therefore  fall 
rapidly,  while  if  the  number  of  nuclei  be  large,  since  there  is 
only  the  same  quantity  of  water  to  be  distributed  among  them, 

TIME  TAKEN  BY  FOGS  TO  FALL,  IN  SECONDS. 


Expansion 

Left  side 

Right  side 

Ratio  of  times 
negative  /positive 

1-28 

positive     5 
negative  15 

negative  16 
positive     3 

5-Oj 

1-30 

negative  15 
positive     5 
negative  10 
positive     2 

positive     2 
negative  15 
positive     2 
negative  10 

5-0  f 

5-oJ 

1-31 

positive     7 
negative  14 

negative  12 
positive     7 

"I  1-8 
2-OJ 

1-32 

negative     8 
positive     8 
negative  14 
positive  12 

positive     5 
negative  10 
positive     8 
negative  17 

1-6 

1-5 
1-7 

1-4 

1-33 

negative  12 
positive  12 

positive  10 
negative  13 

;>15 

1-35 

negative  10 
positive  10 

positive  10 
negative  10 

13w  . 

the  drops  will  be  small  and  will  fall  slowly.     In  the  experiments 
referred  to  in  the  table  there  was  a  potential  difference  equal 

10—2 


148         ON   SOME  PHYSICAL  PROPERTIES  OF  GASEOUS   IONS.          [81 

to  that  due  to  two  Leclanche  cells  between  the  middle  plate 
and  either  of  the  outer  ones.  The  words  positive  and  negative 
in  the  table  indicate  that  the  positive  or  negative  ions  respec- 
tively were  in  excess  in  the  region  referred  to. 

The  difference  in  the  rates  of  fall  of  the  drops  with  the 
same  expansions  is  due  to  irregularities  in  the  action  of  the  bulb 
used  to  produce  the  Rontgen  rays.  The  negative  ions  begin  to 
act  as  nuclei  for  foggy  condensation  when  the  expansion  is  about 
1*25,  corresponding  to  about  a  fourfold  supersaturation,  while  we 
see  from  the  table  that  the  positive  ions  do  not  begin  to  act 
as  nuclei  until  the  expansion  is  equal  to  1'31,  corresponding  to 
about  a  sixfold  supersaturation.  Wilson  has  shown  that  all  the 
negative  ions  are  caught  when  the  expansion  is  equal  to  1'28, 
but  that  it  is  not  until  the  expansion  reaches  1*35  that  all  the 
positive  ions  are  caught.  This  is  not  due  to  the  negative  ions 
having  a  larger  electrical  charge  than  the  positive ;  to  show  this, 
take  an  expansion  vessel  such  as  that  shown  in  Fig.  36  and  ionise 
the  gas  in  it  by  Rontgen  rays ;  first  produce  a  fog  with  an  ex- 
pansion of  1'28  (which  only  brings  down  the  negative  ions),  and 
determine  the  number  of  ions  from  the  time  of  fall  in  the  way 
explained  on  page  124 ;  then  with  the  same  intensity  of  radiation 
produce  a  cloud. by  an  expansion  of  1*35,  which  brings  down  both 
the  positive  and  negative  ions,  and  again  calculate  the  number 
of  ions ;  we  shall  find  it  twice  as  great  as  in  the  .first  case,  thus 
showing  that  the  numbers  of  positive  and  negative  ions  are  equal. 
As  the  gas  as  a  whole  has  no  charge,  the  total  charge  on  the 
positive  ions  must  be  equal  to  that  on  the  negative,  hence  as 
there  are  as  many  positive  ions  as  negative,  the  charge  on  a  posi- 
tive ion  must  be  the  same  as  that  on  a  negative  one.  We  shall 
return  to  the  origin  of  the  greater  efficiency  of  the  negative 
than  of  the  positive  ions  when  we  discuss  the  theory  of  the 
action  of  ions  in  promoting  condensation.  In  the  meantime  we 
may  point  out  that  this  difference  between  the  ions  may  have  very 
important  bearings  on  the  question  of  atmospheric  electricity,  for  if 
the  ions  were  to  differ  in  their  power  of  condensing  water  around 
them*¥hen  we  might  get  a  cloud  formed  round  one  set  of  ions 
and  not  round  the  other.  The  ions  in  the  cloud*  would  fall  under 
gravity,  and  thus  we  might  have  separation  of  the  positive  and 
the  negative  ions  and  the  production  of  an  electric  field,  the  work 


82]  ON    SOME   PHYSICAL    PROPERTIES   OF   GASEOUS   IONS.          149 

required  for  the  production  of  the  field  being  done  by  gravity*. 
An  action  of  this  kind  would  tend  to  make  the  charge  in  the  air 
positive,  as  more  negative  ions  than  positive  would  be  carried 
down  by  water  drops:  for  a  further  consideration  of  this  effect 
we  may  refer  the  reader  to  the  papers  by  Elster  and  Geitelf  on 
the  ionic  theory  of  atmospheric  electricity. 

82.  Theory  of  the  effect  of  ions  on  Condensation.  The  effect 
of  electrification  on  the  evaporation  of  drops  of  water  was  in- 
vestigated by  the  writer  in  Applications  of  Dynamics  to  Physics 
and  Chemistry,  p.  165.  The  general  tendency  of  this  effect  can 
easily  be  seen  from  elementary  principles  :  for  if  we  have  a  drop  of 
water  of  radius  a,  carrying  a  charge  e  of  electricity,  its  potential 
energy  is  equal  to  \e~/Ka,  where  K  is  the  specific  inductive 
capacity  of  the  dielectric  surrounding  the  drop.  Now  as  the  drop 
evaporates  the  electricity  remains  behind,  so  that  e  does  not 
change  while  a  diminishes,  hence  the  potential  energy  due  to 
the  electrification  of  the  drop  increases  as  the  drop  evaporates; 
thus  to  make  the  drop  evaporate  when  charged  more  work  has 
to  be  available  than  when  it  is  uncharged,  so  that  electrification 
will  diminish  the  tendency  of  the  drop  to  evaporate,  and  the  drop 
will  be  in  equilibrium  when  the  vapour  pressure  of  the  water 
vapour  around  it  would  not  be  sufficient  to  prevent  the  evaporation 
of  an  uncharged  drop.  The  surface  tension  of  the  water  will,  as 
was  shown  by  Lord  Kelvin,  produce  the  opposite  effect  ;  for  the 
potential  energy  due  to  the  surface  tension  is  equal  to  4>7ra?T, 
where  T  is  the  surface  tension;  thus  as  the  drop  evaporates 
the  energy  due  to  surface  tension  diminishes,  so  that  the  work 
required  to  vaporise  a  given  quantity  of  water  is  less  than  if 
surface  tension  were  absent,  or,  what  is  the  same  thing,  as  if  the 
surface  were  flat.  Thus  a  curved  drop  will  evaporate  when  a  flat 
one  would  be  in  equilibrium. 

It    is   shown   in  Applications   of  Dynamics   to   Physics   and 
Chemistry,  p.  165,  that  when  &p,  the  change  in  the  vapour  pres- 
sure due  to  the  electrification  and  surface  tension,  is  only  a  small 
fraction  of  the  original  vapour  pressure  p, 
gp==JL_f2T_      #     \ 
~~ 


__  _ 

p      RO  \  a       87rKa*}  a-  -  p  ' 

*  J.  J.  Thomson,  Phil.  Mag.  v.  46,  p.  528,  1898. 

t  Elster  and  Geitel,  Ptiysikalische  Zeitschrift,  i.  p.  245,  1900. 


150         ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          [82 

cr  is  the  density  of  water,  p  that  of  the  vapour,  6  the  absolute 
temperature,  R  the  constant  which  occurs  in  the  equation  for 
a  '  perfect'  gas,  p  =  Rdp  ;  in  the  investigation  this  equation  is 
assumed  to  hold  for  the  water  vapour.  When  the  change  in  the 
pressure  is  not  a  small  fraction  of  the  equilibrium  vapour  pressure 
for  an  infinitely  large  drop,  then  the  investigation  already  alluded 
to  shows  that  the  preceding  equation  has  to  be  replaced  by 

Mlocr  P 

log*      4 


where  p  and  p  are  the  equilibrium  vapour  pressure  and  density 
for  a  drop  of  radius  a,  P  and  p'  the  corresponding  quantities  for 
a  drop  of  infinite  radius.  Since  p'  —  p  is  small  compared  with  a-, 
this  equation  becomes  approximately 


We  see  from  this  equation  that  if  e  is  zero  the  equilibrium 
vapour  pressure  p  for  a  drop  of  finite  size  is  always  greater  than  P, 
so  that  such  a  drop  would  evaporate  unless  the  vapour  around 
it  were  supersaturated ;  when  however  the  drop  is  electrified  this 
is  no  longer  the  case,  for  we  see  from  equation  (1)  that  in  this 
case  if  the  vapour  is  saturated,  i.e.  if  the  vapour  pressure  is  P,  the 
drop  will  grow  until  its  radius  a  is  given  by  the  equation 

2T 


a       SirKa4 


=  0. 


Thus  if  the  drop  were  charged  with  the  quantity  of  electricity 
carried  by  a  gaseous  ion,  i.e.  3'4  x  10~10  electrostatic  units,  and  if 
the  surface  tension  of  the  small  drop  had  the  value  76,  which  is  the 
value  for  thick  water  films,  then  a  would  be  equal  to  l/3'2  x  107, 
and  thus  each  gaseous  iou  would  be  surrounded  by  a  drop  of 
water  of  this  radius;  if  we  call  this  radius  c,  then  equation  (1) 
may  be  written 

R6c  loge^  =  2Tx(l-x?) (2), 

where  x  =  cja.  This  equation  enables  us  to  find  $he  size  of  a  drop 
corresponding  to  any  vapour  pressure. 

For  water  vapour  at  10°  C.,  RB  is  equal  to  T3  x  109.     Putting 


83]  ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          151 

for  c  the  value  previously  found  and  T=  76,  equation  (2)  becomes 
approximately 


(3). 


From  this  equation  we  see  that  even  in  a  space  far  from  saturated 
with  water  vapour,  i.e.  when  p  is  only  a  fraction  of  P,  drops  will  be 
formed,  and  that  the  size  of  these  drops  diminishes  only  very  slowly 
as  the  quantity  of  water  vapour  in  the  surrounding  air  diminishes  ; 
thus,  if  we  diminish  the  quantity  of  water  vapour  in  the  air  to 
I/e,  i.e.  1/2*7  of  that  required  to  saturate  it,  we  see  from  equation 
(3)  that  the  radius  of  the  drops  formed  round  the  ions  would  only 
be  a  little  less  than  10/11  of  the  radius  of  the  drop  formed  in 
saturated  air  :  and  that  to  reduce  the  drop  to  half  the  radius 
corresponding  to  saturation,  we  should  have  to  dry  the  air  so 
completely  that  p/P  was  only  about  1/3  x  1016.  We  have  seen  that 
there  are  always  ions  present  in  the  air,  hence  there  will  always 
be  small  drops  of  water  present  if  there  is  any  water  vapour  in  the 
air  ;  if,  as  has  been  suggested,  these  drops  play  a  part  in  certain 
cases  of  chemical  combination,  the  preceding  numerical  example 
will  show  the  difficulty  of  getting  the  gas  dry  enough  to  produce 
a  substantial  reduction  in  the  volume  of  these  charged  drops. 

83.  Supersaturation  required  to  make  one  of  the  charged  drops 
grow  to  a  large  size.  As  the  radius  of  the  drop  increases  from  c 
to  an  infinite  size,  x  diminishes  from  unity  to  zero.  Now  the  right- 
hand  side  of  equation  (2)  vanishes  at  each  of  these  limits,  but 
between  them  it  reaches  a  maximum  value  which  occurs  when 

4-tf3  =  1  or  x  —  -      ,  when  x(l  —a?)  reaches  the  value  '471  ;  hence 
I'oo 

we  see  from  equation  (3)  that  for  the  drops  to  increase  to  a  large 
size  \ogep/P  must  reach  the  value  1/7  approximately.  Hence  for 
the  drops  to  grow  p/P  must  be  about  5*3  :  this,  on  the  theory  we 
have  given,  is  the  amount  of  supersatu  ration  required  to  make 
large  drops  grow  round  the  ions.  We  have  seen  from  Wilson's 
experiment  that  it  actually  requires  a  four-  fold  supersaturation, 
but  as  in  the  theory  the  saturated  water  vapour  was  assumed  to 
obey  Boyle's  law,  and  the  surface  tension  was  assumed  to  have 
the  value  it  has  for  thick  films,  neither  of  which  assumptions 
is  likely  to  be  true,  the  agreement  between  the  theory  and  the 
experiments  is  as  close  as  could  be  expected. 


152          ON   SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          [84 

84.  Wilson  showed  that  even  when  there  is  no  external  ionisa- 
tion  a  dense  cloud,  the  nuclei  of  which  are  not  charged,  is  produced 
by  an  eight-fold  supersaturation  :  we  can  by  the  aid  of  equation  (1) 
determine  the  radii  of  these  nuclei,  supposed  spherical ;  putting 
in  that  equation  e  =  0,  T=  76,  R6  =  1'3  x  109,  and  p/P  =  8,  we 
find  that  a,  the  radius  of  the  nucleus  which  produces  this  kind 
of  condensation,  is  equal  to  1/1*9  x  107.      This  nucleus  is   thus 
slightly  larger  than  the  drop  which  collects  round  an  ion,  as  we 
found  that  the  radius  of  this  drop  is  l/3'l  x  107.     With  regard 
to  the  nature  of  the  nuclei  which  produce  the  cloud  corresponding 
to  the   eight- fold   supersaturation,   Wilson  has  proved  that  the 
amount  of  supersaturation  required  to  produce  the  cloud  is  the 
same  in   air,  oxygen,  hydrogen,  and   carbonic  acid;   the  size  of 
the  nuclei  is  therefore  the  same  in  all  these  gases ;  it  is  thus  very 
improbable  that  they  consist  of  aggregations  of  the  molecules  of 
the  gas,  it  would  seem  most  likely  that  they  are  minute  drops 
of  water  which  are  continually  being  formed  from  the  saturated 
vapour   and    then   evaporating,  but    lasting   sufficiently   long  to 
enable  them   to  be  caught  during   the   sudden    expansion,  and 
to  act  as  the  nuclei  round  which  the  drops  in  the  cloud  condense. 
These  minute  drops  of  water  are  not  however  all  of  the  same 
size,  for  after  passing  the  expansion  1*38  the  density  of  the  cloud 
increases  very  rapidly  as  the  expansion  increases,  showing  that 
many  more  nuclei  become  efficient  when  the  expansion  increases. 
This  behaviour  of  the  cloud  indicates  that  there  are  little  drops 
of  water  of  different  sizes,  the  small  ones  being  more  numerous 
than  the  larger  ones,  and  that  there  is  a  fairly  definite  limit  to 
the  size  of  the  drop,  the   number  of  drops  whose  size  exceeds 
this  limit  being  too  small  to  produce  an  appreciable  cloud.     This 
collection  of  drops  of  different  sizes  is  what  we  might  expect  if 
we  regard  the  little  drops  as  arising  from  coalescence  of  molecules 
of  water  vapour,  and  the  larger  drops  from  the  coalescence  of  the 
smaller  ones. 

85.  The  fact  that  the  drops  are  of  different  sizes  indicates  that 
they  are  not  in  a  state  of  equilibrium  with  regard  to  evaporation 
and  condensation,  and  the  drops  have  probably  a  very  ephemeral 
existence.     It  may  however  be  pointed  out  that  on  the  view  of 
the  relation  between  surface  tension  and  the  thickness  of  water 
films,  to  which  Reinold  and  Riicker  were  led  by  their  experi- 


86] 


ON    SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS. 


153 


ments  on  very  thin  films,  drops  of  pure  water  of  a  definite  radius 
might  be  in  equilibrium  with  saturated  water  vapour  even  if  they 
were  not  charged.  For  according  to  these  physicists  the  relation 
between  the  surface  tension  and  the  thickness  of  the  film  is  re- 
presented by  a  curve  of  the  type  shown  in  Fig.  39,  the  ordinates 


Thickness 


Fig.  39. 

representing  the  surface  tension  and  the  abscissae  the  thickness 
of  the  film  :  this  curve  shows  maxima  and  minima  values  for  the 
surface  tension. 

Now  consider  the  case  of  a  drop  whose  diameter  is  a  little 
greater  than  OM ;  in  this  case  as  the  radius  of  the  drop  increases 
the  surface  tension  diminishes ;  the  potential  energy  due  to  surface 
tension  is  proportional  to  the  product  of  the  surface  tension  T 
and  the  area  of  the  surface  4?ra2;  hence  if  we  can  find  a  point 

dT          2T 

between  Q  and  T  where  S  (T .  4?ra2)  =  0  or  T    =  —    —  ,  any  small 

change  in  the  size  of  the  drop  would  not  be  accompanied  by  a 
change  in  the  potential  energy  due  to  surface  tension.  Thus 
surface  tension  would  not  affect  the  conditions  of  equilibrium 
between  the  liquid  and  the  water  vapour,  so  that  if  the  volume 
were  saturated  with  equilibrium  the  drop  would  be  in  equi- 
librium. 

86.  We  have  seen  that  water  vapour  condenses  more  easily 
on  a  negative  than  on  a  positive  ion,  while  the  velocity  of  the 
negative  ion  under  a  given  electric  field  is  greater  than  that  of 
the  positive  ion  :  the  second  result  seems  to  indicate  that  the 
size  of  the  system,  consisting  of  the  negative  ion  and  whatever  may 
be  attached  to  it,  is  smaller  than  the  system  for  the  positive  ion, 


154          ON    SOME   PHYSICAL   PROPERTIES   OF   GASEOUS   IONS.          [86 

while  the  first  indicates  that  it  is  larger.  We  must  remember, 
however,  that  the  velocity  of  an  ion  under  an  electric  field  is  the 
average  velocity  estimated  for  the  life  of  an  ion.  Now  we  have 
seen  that  the  negative  ion  when  first  liberated  is  what  we  have 
called  a  corpuscle,  and  its  mass  is  exceedingly  small  compared 
with  that  of  the  positive  ion;  thus  at  first  the  velocity  of  the 
negative  ion  will  be  greater  than  that  of  the  positive,  but  in 
consequence  of  its  greater  mobility  the  negative  ion  is  more 
likely  than  the  positive  to  attach  itself  to  foreign  bodies  in  its 
neighbourhood,  say  to  those  minute  drops  of  water  which  an 
expansion  greater  than  T38  brings  into  evidence  ;  thus  though 
the  negative  ion  starts  by  being  smaller  than  the  positive,  it  may 
before  it  recombines  with  a  positive  ion  to  form  a  neutral  system 
have  become  the  centre  of  an  aggregation  greater  than  that 
surrounding  the  positive  ion.  The  efficiency  of  an  ion  as  a 
nucleus  for  condensation  depends  upon  the  maximum  size  of 
the  aggregation,  while  the  velocity  under  the  electric  field  depends 
upon  the  average  size ;  the  average  size  of  a  negative  ion  may 
easily  be  less  than  that  of  a  positive  ion,  since  the  negative  is 
so  much  smaller  to  begin  with,  while  the  greater  mobility  of  the 
negative  is  likely  to  make  it  in  the  end  the  centre  of  a  larger 
system  than  the  positive. 


CHAPTER    VIII. 

IONISATION   BY   INCANDESCENT   SOLIDS. 

87.  WE  shall  now  proceed  to  the  study  of  some  special  cases  of 
ionisation,  beginning  with  that  due  to  incandescent  metals.  That 
the  air  in  the  neighbourhood  of  red-hot  metals  is  a  conductor 
of  electricity  has  been  known  for  nearly  two  centuries  ;  the  earliest 
observations  seem  to  have  been  made  by  Du  Fay*  in  1725,  by  Du 
Tourf  in  1745,  by  Watsonj  in  1746,  by  Priestley§  in  1767,  and 
by  Cavallojl  in  1785.  Becquerellj  in  1853  showed  that  air  at 
a  white  heat  would  allow  electricity  to  pass  through  it  even  when 
the  potential  difference  was  only  a  few  volts.  Blondlot**  confirmed 
and  extended  this  result,  and  proved  that  air  at  a  bright  red  heat 
was  unable  to  insulate  under  a  difference  of  potential  as  low  as 
1/1000  of  a  volt ;  he  showed,  too,  that  the  conduction  through 
the  hot  gas  was  not  in  accordance  with  Ohm's  law.  Recent 
researches  have  thrown  so  much  light  on  the  causes  at  work  in  the 
ionisation  of  gases  in  contact  with  glowing  solids,  that  it  is  un- 
necessary to  enter  into  these  earlier  investigations  in  greater 
detail.  Guthrieff  seems  to  have  been  the  first  to  call  attention  to 
one  very  characteristic  feature  of  ionisation  by  incandescent  metals, 
i.e.  the  want  of  symmetry  between  the  effects  of  positive  and  nega- 
tive electrification.  He  showed  that  a  red-hot  iron  ball  in  air 
could  retain  a  charge  of  negative  but  not  of  positive  electrification, 
while  a  white-hot  ball  could  not  retain  a  charge  of  either  positive 
or  negative  electrification. 

*  Du  Fay,  Mem.  de  VAcad.  1733. 

t  Du  Tour,  Mem.  de  Mathematique  et  de  Physique,  xi.  p.  246,  1755. 

£  Watson,  Phil.  Trans,  abridged,  vol.  x.  p.  296. 

§  Priestley,  History  of  Electricity,  p.  579. 

||   Cavallo,  Treatise  on  Electricity,  vol.  i.  p.  324. 

H  Becquerel,  Annales  de  Chimie  et  de  Physique,  iii.  39,  p.  355,  1853. 
**  Blondlot,  Comptes  Rendus,  xcii.  p.  870,  1881 ;  civ.  p.  283,  1887. 
ft  Guthrie,  Phil.  Mag.  iv.  46,  p.  257,  1873. 


156 


IONISATION    BY    INCANDESCENT   SOLIDS. 


[88 


88.  The  ionisation  produced  by  incandescent  metals  was  in- 
vestigated systematically  in  great  detail  by  Elster  and  Geitel*, 
who  used  for  this  purpose  the  apparatus  represented  in  Fig.  40. 


Battery 


To  Electrometer 


Battery 


Fig.  40. 

This  is  a  glass  vessel  containing  an  insulated  metal  plate  A, 
which  is  connected  with  one  pair  of  quadrants  of  an  electrometer. 
Underneath  this  plate  there  is  a  fine  metallic  wire,  which  can 
be  raised  to  incandescence  by  an  electric  current  passing  through 
the  leads  C,  D ;  to  prevent  any  disturbing  effects  arising  from  the 
change  produced  by  the  current  in  the  electric  potential  of  the 
wire,  the  middle  point  of  the  wire  was  connected  with  the  earth. 
Let  us  first  take  the  case  when  the  gas  in  the  vessel  is  air  or 
oxygen  at  atmospheric  pressure,  then,  as  soon  as  the  glow  of 
the  hot  wire  begins  to  be  visible,  the  metal  plate  receives  a 
positive  charge  ;  this  charge  increases  until  the  potential  of  the 
plate  reaches  a  value  which  varies  very  much  with  the  dimensions 
of  the  apparatus  used :  in  Elster  and  Geitel's  experiments  it  was  of 
the  order  of  a  few  volts.  This  potential  increases  as  the  tempera- 
ture of  the  wire  increases,  until  the  wire  is  at  a  yellow  heat ;  at 

*  Elster  and  Geitel,  Wied.  Ann.  xvi.  p.  193, 1882 ;  xix.  p.  588,  1883 ;  xxii.  p.  123, 
1884;  xxvi.  p.  1,  1885;  xxxi.  p.  109,  1887;  xxxvii.  p.  315, 1889.  Wien.  Berich.  xcvii. 
p.  1175,  1889. 


89]  IONISATION    BY    INCANDESCENT   SOLIDS.  157 

this  stage  the  potential  of  the  plate  is  a  maximum.  After  passing 
this  stage  the  potential  diminishes  as  the  wire  gets  hotter  and 
hotter,  until  at  a  bright  white  heat  the  charge  received  by  the 
plate  is  very  small. 

The  electrification  on  the  plate  is  very  much  influenced  by  the 
pressure  of  the  gas.  Starting  at  atmospheric  pressure  and  gradually 
exhausting  the  vessel,  we  find  that  at  first  the  change  of  pressure 
does  not  produce  any  great  effect  upon  the  potential  of  the  plate  A, 
but  when  we  approach  very  high  exhaustions,  such  as  those  in 
Crookes'  tubes,  the  potential  of  the  plate  begins  to  diminish,  until  at 
very  low  pressures  it  changes  sign  and  may  as  the  exhaustion  pro- 
ceeds reach  a  very  large  negative  value.  The  pressure  at  which  the 
change  in  sign  of  the  electrification  of  the  plate  takes  place  depends 
upon  the  temperature  of  the  wire,  the  higher  the  temperature  the 
higher  the  pressure  at  which  the  reversal  of  the  electrification 
occurs.  Again,  long-continued  incandescence  of  the  wire  favours 
the  negative  electrification  of  the  plate ;  the  physical  condition  of 
the  platinum  wire  is  changed  by  long-continued  heating,  and  the 
wire  becomes  brittle.  The  following  experiment,  due  to  Elster 
and  Geitel  *,  seems  to  indicate  that  the  gases  absorbed  in  the 
platinum  wire  and  which  are  gradually,  bui;  only  very  gradually, 
expelled  by  long-continued  heating,  play  a  considerable  part  in 
the  electrical  phenomena  connected  with  the  incandescence  of 
metals.  They  found  that  if  the  platinum  wire  was  kept  glowing 
in  a  fairly  good  vacuum  long  enough  for  the  metal  plate  to  receive 
a  negative  charge,  the  introduction  of  a  very  small  quantity  of 
fresh  gas  reversed  the  sign  of  electrification  on  the  metal  plate, 
and  the  pressure  had  to  be  reduced  far  below  the  original  value  for 
the  negative  electrification  to  be  recovered. 

89.  The  effects  are  also  complicated  by  the  dust  and  vapour 
given  off  by  the  glowing  platinum,  and  which  form  a  deposit  on  the 
walls  of  the  vessel.  The  production  of  this  dust  can  very  easily  oe 
shown  by  the  study  of  clouds  formed  by  the  method  described  in 
Chapter  VII.  If  a  fine  platinum  wire  is  fused  into  the  expansion 
apparatus,  and  the  air  rendered  dust-free  in  the  usual  way,  so  that 
no  clouds  are  produced  by  an  expansion  less  than  1*25,  dense 
clouds  will  be  formed  by  comparatively  small  expansions  after 
a  current  has  been  sent  through  the  wire  strong  enough  to  raise  it 
*  Elster  and  Geitel,  Wien.  Berich.  xcvii.  p.  1175,  1889. 


158  IONISATION   BY   INCANDESCENT  SOLIDS.  [90 

to  incandescence* ;  indeed  it  is  not  necessary  to  make  the  wire  so 
hot  as  to  be  luminous,  an  increase  in  the  temperature  of  the 

wire  to  200  or  300°  C.  is  sufficient  to  produce  the  cloud. 

t 
The  sign  of  the  electrification  produced  by  glowing  substances 

is  influenced  by  the  nature  of  the  substances  and  of  the  gas 
surrounding  them  ;  thus  in  hydrogen  Elster  and  Geitelf  showed 
that  the  plate  above  the  incandescent  wire  became  negatively 
electrified  even  when  the  hydrogen  was  at  atmospheric  pressure. 
This  electrification  continually  increased  with  the  temperature. 
To  get  the  negative  electrification,  however,  the  wire  must  be  at 
least  at  a  bright  yellow  heat ;  at  lower  temperatures  the  electrifica- 
tion is  positive  ;  a  clean  copper  wire,  on  the  other  hand,  gives  a 
positive  electrification  in  hydrogen,  unless  the  pressure  is  very  low. 

Elster  and  Geitel  showed  that  the  sign  of  the  electrification 
in  water  vapour  and  the  vapours  of  sulphur  and  phosphorus  was 
the  same  as  in  air ;  they  could  detect  no  electrification  in  mercury 
vapour. 

90.  The  influence  of  the  nature  of  the  incandescent  substance 
is  shown  by  the  fact  that  with  incandescent  carbon  filaments  the 
electrification  on  the  metal  plate  is  always  negative.     It  is  also 
shown  clearly  by  some  experiments  made  by  BranlyJ.     Branly's 
method  was  as  follows  :  he  hung  up  a  charged  insulated  conductor 
in  the  neighbourhood  of  the  incandescent  body  ;   he  found  that 
when  the  latter  was  a  piece  of  platinum  at  a  dull  red  heat  the 
insulated  conductor  lost  a  negative  but  not  a  positive  charge;  when 
the  platinum  was  white  hot  the  conductor  was  discharged  whether 
electrified  positively  or  negatively.     If  the  incandescent  body  was 
an  oxide  and  not  a  pure  metal,  at  any  rate  if  it  was  an  oxide  of 
one  of  the  metals  tried  by  Branly,  viz.  lead,  aluminium  or  bismuth, 
then  it  would  discharge  a  positively  electrified  body  but  not  a 
negatively  electrified  one,  which  is  exactly  opposite  to  the  effect 
produced  by  a  pure  metal  at  a  dull  red  heat. 

91.  McClelland§  sucked  the  gases  from  the  neighbourhood  of 
the  incandescent  wire  and  then  investigated  their  properties.     He 

*  K.  v.  Helmholtz,  Wied.  Ann.  xxxii.  p.  1,  1887.    Lodge,  Nature,  xxxi.  p.  267, 
1884. 

t  Elster  and  Geitel,  Wied.  Ann.  xxxi.  p.  109,  1887. 

t  Branly,  Comptes  Eendus,  cxiv.  p.  1531,  1892. 

§  McClelland,  Proc.  Camb.  Phil.  Soc.  x.  p.  241,  1900.  * 


92]  IONISATION   BY   INCANDESCENT   SOLIDS.  159 

found  that  as  soon  as  the  wire  began  to  glow  the  gas  would 
discharge  a  negatively  but  not  a  positively  electrified  body;  when 
the  temperature  of  the  electrified  body  was  increased  by  about 
400°  C.,  the  gas  began  to  discharge  a  positively  electrified  body, 
though  not  so  freely  as  it  did  a  negatively  electrified  one  ;  when 
the  wire  got  to  a  bright  yellow  heat  the  gas  discharged  both 
positive  and  negative  electricity  with  equal  facility.  McClelland 
investigated  the  laws  of  conduction  of  electricity  through  the  gas 
which  had  been  in  contact  with  the  glowing  wire;  he  found  that  it 
showed  all  the  characteristics  of  conduction  through  a  gas  contain- 
ing ions ;  thus  the  relation  between  the  current  and  the  electro- 
motive force  is  represented  by  a  curve  like  Fig.  5,  the  current 
soon  reaching  saturation.  McClelland  also  determined  the  velocity 
in  an  electric  field  of  the  ions,  produced  by  the  incandescent  metal. 
He  found  that  their  velocity  was  small  compared  with  that  of  the 
ions  produced  by  Rontgen  rays,  and  that  the  hotter  the  wire  the 
smaller  was  the  velocity  of  the  ions. 

92.  The  account  we  have  already  given  of  the  effects  observed 
in  the  neighbourhood  of  an  incandescent  wire  shows  that  the 
electrification  produced  in  this  way  is  a  very  complicated  pheno- 
menon, and  depends  : 

(1)  On  the  temperature  of  the  wire. 

(2)  On  the  pressure  of  the  gas  around  the  wire. 

(3)  On  the  nature  of  the  gas. 

(4)  On  the  nature  of  the  incandescent  wire. 

We  shall  simplify  the  investigation  of  the  cause  of  this  electrifi- 
cation if  we  study  a  case  in  which  as  many  as  possible  of  these 
effects  are  eliminated.  Now  (2)  and  (3)  are  eliminated  if  we  work 
with  the  highest  attainable  vacuum  ;  in  this  case  the  phenomena 
are  greatly  simplified  and  exhibit  points  of  remarkable  interest. 
To  investigate  them  we  may  use  a  piece  of  apparatus  like  that 
shown  in  Fig.  41.  It  consists  of  a  straight  piece  of  fine  wire  AB, 
which  can  he  heated  to  any  desired  temperature  by  an  electric 
current  led  hi  through  the  leads  CA,  DB.  Around  this  wire  and 
insulated  from  it  is  a  metallic  cylinder,  shown  in  section  in  EF  and 
GH;  this  cylinder  should  be  longer  than,  and  coaxial  with,  the 
wire.  This  system  is  sealed  into  a  glass  vessel  connected  with  an 
air  pump  and  the  pressure  reduced  as  low  as  possible,  say  to 


160  IONISATION   BY   INCANDESCENT  SOLIDS.  [93 

•001  mm.  of  mercury.     It  is  desirable  to  keep  the  wire  red  hot  for 
a  very  considerable  time  (I  have  found  a  week  not  too  long),  in 


Fig.  41. 

order  to  expel  gases  absorbed  in  the  wire ;  until  these  are  got  rid 
of  the  behaviour  of  the  wire  is  very  irregular.  The  vessel  should 
be  pumped  from  time  to  time  while  the  wire  is  hot,  to  get 
rid  of  the  gases  coming  out  of  the  wire;  it  will  be  necessary 
to  exhaust  the  vessel  from  time  to  time,  even  after  these  have 
been  expelled,  as  the  heat  coming  from  the  wire  seems  to  liberate 
gas  from  the  walls  of  the  glass  vessel  and  the  metal  cylinder. 
Connect  the  hot  wire  to  one  terminal  of  a  battery  and  the  cylinder 
to  the  other,  and  place  in  the  circuit  a  sensitive  galvanometer.  If 
now  the  wire  be  made  red  hot  and  connected  with  the  negative 
pole  of  the  battery,  an  appreciable  current  will  go  through  the 
galvanometer ;  if,  however,  the  terminals  are  reversed  so  that  the 
hot  wire  is  connected  with  the  positive  pole  of  the  battery,  the 
current  which  passes  is  too  small  to  be  detected  by  the  galvano- 
meter ;  thus  there  can  be  a  current  through  the  exhausted  vessel 
when  the  negative  electricity  goes  from  the  hot  wire  to  the  cold 
cylinder,  but  not  an  appreciable  one  when  the  positive  electricity 
would  have  to  go  from  the  wire  to  the  cylinder ;  the  system  can 
thus  transmit  a  current  in  only  one  direction.  The  current  does 
not  obey  Ohm's  law:  at  first  it  increases  with  the  electromotive 
force,  but  it  soon  reaches  a  saturation  value  beyond  which  it  does 
not  increase,  even  though  the  electromotive  force  is  increased, 
provided  the  increase  is  not  sufficient  to  enable  the  field  itself  to 
ionise  the  gas.  In  some  experiments  made  by  the  author,  about 
10  volts  was  sufficient  to  produce  the  saturation  current. 

93.     The  saturation  current  increases  very  rapidly  with  the 
temperature.     This  is  well  shown  by  the  curve  in  Fig.  42,  which 


93] 


IONISATION   BY   INCANDESCENT   SOLIDS. 


161 


represents  the  results  of  the  experiments  made  by  O.  W.  Richard- 
son*, in  the  Cavendish  Laboratory,  on  the  saturation  current 
between  a  hot  platinum  wire  and  a  metal  cylinder  surrounding  it 


220 
20O 
180 
160 
140 
I  20 


•J  100 
§ 


£ 


SO 

60 

40 

20 


1010       SO 


90        130       /70        2/0 
Temperature  Centigrade. 
Fig.  42. 


in  a  high  vacuum.  The  temperatures  were  obtained  by  measuring 
the  resistance  of  the  wire.  Richardson  found  that  the  relation 
between  the  saturation  current  /  and  the  absolute  temperature 
6  could  be  expressed  by  an  equation  of  the  form 


0.  W.  Richardson,  Proc.  Camb.  Phil.  Soc.  xi.  p.  286,  1902. 


T.  G. 


11 


162 


IONISATION  BY   INCANDESCENT  SOLIDS. 


[94 


for  the  curve  in  Fig.  42, 

a  =  1-51  x  1026,     b  =  4-93  x  104. 

In  the  case  of  this  wire  the  current  amounted  to  about 
4  x  10~4  amperes  at  the  temperature  1500°  C.,  which  represents 
a  rate  of  emission  of  negative  electricity  from  the  hot  wire  of  above 
one  milliampere  per  square  centimetre  of  surface.  If  the  same 
formula  held  up  to  the  melting  point  of  platinum,  which  we  shall 
take  to  be  2000°  C.,  the  rate  of  emission  of  negative  electricity 
from  the  glowing  wire  would  be  about  1/10  of  an  ampere  per 
square  centimetre. 

The  rate  of  escape  of  negative  electricity  from  glowing  carbon 
in  some  cases  greatly  exceeds  that  from  glowing  platinum.  This 
is  no  doubt  chiefly  owing  to  the  fact  that  the  carbon  can  be 
raised  to  a  much  higher  temperature  than  the  platinum. 
Richardson  has  obtained  from  carbon  filaments  in  a  good  vacuum 
currents  of  the  order  of  an  ampere  per  square  centimetre  of 
surface. 

94.  This  escape  of  negative  electricity  from  glowing  carbon  in 
high  vacua  is  the  cause  of  an  effect  observed  in  incandescent  electric 
lamps,  known  as  the  Edison  effect,  and  which  has  been  studied  by 
Preece*  and  in  great  detail  by  Flemingf.  The  'Edison  effect' 


Fig.  43. 

is  as  follows :  Suppose  that  ABC  represents  the  carbon  filament 
of  an   incandescent  lamp,  and   that  an  insulated  metal   plate  is 

*  Preece,  Proc.  Roy.  Soc.  xxxviii.  p.  219,  1885. 

t  Fleming,  Proc.  Roy.  Soc.  xlvii.  p.  118,  1890 ;  Phil.  Mag.  xlii.  p.  52,  1896. 


94]  IONISATION   BY   INCANDESCENT   SOLIDS.  163 

inserted  between  the  filaments ;  then  if  the  positive  end  A  of  the 
filament  is  connected  with  a  wireD  leading  from  the  metallic  plate 
and  a  galvanometer  inserted  between  A  and  D,  a  considerable 
current,  amounting  in  some  of  Fleming's  experiments  to  three  or 
four  milliarnperes,  passes  through  the  galvanometer,  the  direction 
of  the  current  being  from  A  to  D  through  the  galvanometer.  If, 
however,  the  metal  plate  is  connected  with  the  negative  electrode 
of  the  lamp  and  a  galvanometer  inserted  in  this  circuit,  the  current 
through  the  galvanometer  is  exceedingly  small  compared  with  that 
observed  in  the  preceding  case.  We  see  that  this  is  what  would 
occur  if  there  was  a  vigorous  discharge  of  negative  electricity  from 
the  negative  leg  of  the  carbon  filament,  and  no  discharge  or 
a  much  smaller  one  from  the  positive  leg ;  this  would  tend  to 
make  the  potential  of  the  metal  plate  differ  but  little  from  that  of 
the  negative  leg  of  the  carbon  loop,  while  the  difference  of 
potential  between  the  positive  leg  and  the  plate  would  be  nearly 
that  between  the  electrodes  of  the  lamp,  and  consequently  the 
current  through  a  circuit  connecting  the  positive  electrode  to  the 
metallic  plate  would  be  much  greater  than  through  one  connecting 
the  negative  electrode  to  the  plate. 

Fleming  showed  that  when  the  negative  leg  of  the  carbon  loop 
was  surrounded  by  a  cylinder  made  either  of  metal  or  of  an 
insulating  substance,  the  Edison  effect  disappeared  almost  entirely. 
Fleming  too  found,  as  Elster  and  Geitel  had  previously  shown  by 
a  somewhat  different  method,  that  a  current  of  electricity  could 
pass  between  an  incandescent  carbon  filament  arid  a  cold  electrode, 
if  the  direction  of  the  current  was  such  as  to  cause  the  negative 
electricity  to  pass  from  the  hot  filament  to  the  cold  plate,  and  that 
a  current  would  not  pass  in  the  opposite  direction.  Elster  and 
Geitel  showed,  too,  that  a  plate  placed  near  an  incandescent  fila- 
ment received  even  in  very  high  vacua  a  charge  of  negative 
electricity.  The  behaviour  of  the  hot  filament  shows  that  it,  like 
the  incandescent  platinum  wire,  emits  negative  electrification. 
That  the  emission  from  the  carbon  filament  is  much  greater  than 
that  from  the  platinum  wire — great  as  we  have  seen  the  latter  to 
be — is  shown  by  the  fact  that  although,  as  Fleming  (loc.  cit)  has 
shown,  the  'Edison  effect'  can  be  observed  with  an  incandescent 
platinum  wire  in  place  of  the  carbon  filament,  the  effect  with 
platinum  is  exceedingly  small  compared  with  that  with  carbon,  and 

11—2 


164  IONISATION   BY   INCANDESCENT  SOLIDS.  [95 

is  only  appreciable  when  the  platinum  is  so  hot  that  it  is  on  the 
point  of  melting. 

95.  There  can  thus  be  no  doubt  that  from  incandescent  metals 
and  carbon  there  is  a  very  rapid  escape  of  negative  electricity.  The 
question  arises,  What  are  the  carriers  of  this  electrification  ?  The 
answer  to  this  question  seems  at  first  sight  obvious,  for  both  the 
carbon  filament  and  the  platinum  wire  volatilise,  or  at  any  rate 
give  off  dust  if  not  vapour  at  high  temperatures.  This  is  shown 
by  the  familiar  deposit  of  carbon  on  the  glass  of  incandescent 
lamps,  and  of  platinum  or  platinum  oxide  on  the  walls  of  an 
exhausted  vessel  in  which  a  platinum  wire  has  been  glowing  for 
a  long  period.  It  seems  natural,  therefore,  to  regard  the  carriers 
of  the  negative  electricity  as  the  molecules  or  atoms  of  carbon 
or  platinum  vapour.  We  might,  however,  be  led  to  suspect  the 
accuracy  of  this  view  when  we  observe  the  enormous  quantities  of 
negative  electricity  which  can  be  discharged  by  a  small  piece  of 
very  thin  wire ;  quantities  which  are  inconsistent  with  that  law  of 
electrolysis  which  states  that  to  carry  a  quantity  of  electricity  E 
we  require  a  mass  of  a  substance  Ee,  where  e  is  the  electrochemical 
equivalent  of  the  substance. 

We  can,  however,  determine  by  the  method  of  Art.  51  the 
ratio  of  the  charge  e  to  the  mass  m  of  the  carriers  of  the 
negative  electricity  from  an  incandescent  wire.  The  results  of 
this  determination,  which  are  given  in  Art.  51,  are  conclusive, 
for  they  show  that  the  value  of  e/m  for  these  carriers  is  the 
same  as  its  value  for  the  carriers  of  the  negative  electricity  in  the 
cathode  rays,  and  in  the  discharge  of  negative  electricity  from 
metals  placed  in  a  good  vacuum  and  illuminated  by  ultra-violet 
light.  Thus  the  negative  electricity  from  the  hot  wire  is  carried 
by  the  same  carriers  as  the  cathode  rays,  i.e.  by  '  corpuscles,'  those 
small  negatively  electrified  bodies  of  constant  mass  which  in  all 
the  cases  yet  investigated  act  as  the  carriers  of  negative  electricity 
in  high  vacua. 

We  thus  are  led  to  the  conclusion  that  from  an  incandescent  metal 
or  glowing -piece  of  carbon  '  corpuscles '  are  projected,  and  though  we 
have  as  yet  no  exact  measurements  for  carbon,  the  rate  of  emission 
must,  by  comparison  with  the  known  much  smaller  rate  for  plati- 
num, amount  in  the  case  of  a  carbon  filament  at  its  highest  point  of 


95]  IONISATION   BY   INCANDESCENT   SOLIDS.  165 

incandescence  to  a  current  equal  to  several  amperes  per  square 
centimetre  of  surface.  This  fact  may  have  an  important  applica- 
tion to  some  cosmical  phenomena,  since,  according  to  the  generally 
received  opinion,  the  photosphere  of  the  sun  contains  large, 
quantities  of  glowing  carbon;  this  carbon  will  emit  corpuscles 
unless  the  sun  by  the  loss  of  its  corpuscles  at  an  earlier  stage 
has  acquired  such  a  large  charge  of  positive  electricity  that  the 
attraction  of  this  is  sufficient  to  prevent  the  negatively  electrified 
particles  from  getting  right  away  from  the  sun ;  yet  even  in  this 
case,  if  the  temperature  were  from  any  cause  to  rise  above  its 
average  value,  corpuscles  would  stream  away  from  the  sun  into  the 
surrounding  space.  We  may  thus  regard  the  sun,  and  probably 
any  luminous  star,  as  a  source  of  negatively  electrified  particles 
which  stream  through  the  solar  and  stellar  systems.  Now  when 
corpuscles  moving  at  a  high  speed  pass  through  a  gas  they  make 
it  luminous ;  thus  when  the  corpuscles  from  the  sun  meet  the 
upper  regions  of  the  earth's  atmosphere  they  will  produce 
luminous  effects.  Arrhenius*  has  shown  that  we  can  explain  in 
a  satisfactory  manner  many  of  the  periodic  variations  in  the 
Aurora  Borealis  if  we  assume  that  it  is  caused  by  corpuscles 
from  the  sun  passing  through  the  upper  regions  of  the  earth's 
atmosphere. 

The  emission  of  corpuscles  from  incandescent  metals  and 
carbon  is  readily  explained  by  the  view — for  which  we  find  con- 
firmation in  many  other  phenomena — that  corpuscles  are  dis- 
seminated through  metals  and  carbon,  not  merely  when  these  are 
incandescent,  but  at  all  temperatures ;  the  corpuscles  being  so 
small  are  able  to  move  freely  through  the  metal,  and  they  may 
thus  be  supposed  to  behave  like  a  perfect  gas  contained  in  a 
volume  equal  to  that  of  the  metal.  The  corpuscles  a*e  attracted 
by  the  metal,  so  that  to  enable  them  to  escape  into  the  space 
surrounding  it  they  must  have  sufficient  kinetic  energy  to  carry 
them  through  the  layer  at  its  surface,  where  its  attraction 
of  the  corpuscles  is  appreciable.  If  the  average  kinetic  energy 
of  a  corpuscle  like  that  of  the  molecule  of  a  gas  is  proportional 
to  the  absolute  temperature,  then  as  the  temperature  increases, 
more  and  more  of  the  corpuscles  will  be  able  to  escape  from  the 
metal  into  the  air  outside. 

*  Arrhenius,  Physikalische  Zeitschrift,  ii.  pp.  81,  97,  1901. 


166  IONISATION   BY  INCANDESCENT  SOLIDS.  [96 

Rate  at  which  the  corpuscles  escape  from  the  metal. 

96.  We  can  without  much  difficulty  find  an  expression  for 
this  quantity  if  we  assume  that  the  corpuscles  in  the  rnetal  behave 
like  a  perfect  gas.  Let  AB,  CD  represent  two  planes  parallel  to 
the  surface  of  the  metal  including  between  them  the  region  in 
which  the  metal  exerts  an  appreciable  force  upon  the  corpuscle. 
Let  us  take  the  axis  of  x  at  right  angles  to  these  planes,  the  posi- 
tive direction  of  x  being  from  the  air  to  the  metal  ;  then  if  p  is 
the  pressure  due  to  the  corpuscles,  n  the  number  of  corpuscles  in 
unit  volume,  X  the  force  acting  on  a  corpuscle,  we  have  when 
there  is  equilibrium 


«; 


but  if  the  corpuscles  behave  like  a  perfect  gas  p  =  ftOn,  where  6  is 
the  absolute  temperature  and  ft  a  constant  which  is  the  same  for 
all  gases  ;  substituting  this  value  for  p  in  equation  (1),  we  get 


integrating  this  equation  from  CD  to  AB,  we  get 

,      n  w 

lo*;Sr-jg3' 

or  ri=Ne~&  ...........................  (3), 

where  n'  and  N  are  respectively  the  numbers  of  corpuscles  in  unit 
volume  of  the  air  and  metal,  and 

w—  IXdx; 

thus  w  is  the  work  required  to  drag  a  corpuscle  out  of  the  metal. 

Equation  (3)  gives  the  number  of  corpuscles  in  the  air  when 
things  have  attained  a  steady  state.  To  find  the  number  of 
corpuscles  coming  from  the  metal  in  unit  time  let  us  proceed 
as  follows  :  regard  the  steady  state  as  the  result  of  a  dynamical 
equilibrium  between  the  corpuscles  going  from  the  metal  to  the 
air  and  those  going  from  the  air  to  the  metal.  If  ri  is  the 
number  of  corpuscles  in  unit  volume  of  the  air,  the  number  which 


96]  IONISATION   BY   INCANDESCENT   SOLIDS.  167 

in  one  second  strike  against  unit  area  of  the  metal  is  by  the 
Kinetic  Theory  of  Gases  equal  to 

00 

2  udn, 
o 

dn  being  the  number  of  corpuscles  which  have  velocities  between 
u  and  u  +  du,  and  the  summation  is  to  be  taken  for  all  positive 
values  of  u.  Now  if  n'  is  the  total  number  of  corpuscles  in  unit 
volume 


where  m  is  the  mass  of  a  corpuscle  :  hence 


,     /hm  f00 
1  \     ~  ~  I    6~' 

V      7T    Jo 


2  udn  —  nf  \  /  -  -  I    e-hmu*udu 
1 


c 


where  c  is  the  velocity  of  mean  square  and  is  equal  to  a  (0/m)l, 
a  being  a  constant  which  is  the  same  for  all  gases  :  substituting 
the  value  of  n  from  equation  (3)  we  find  that  the  number  of 
corpuscles  coming  from  the  air  and  striking  against  unit  area  of 
the  metal  in  unit  time  is  equal  to 


if  we  suppose  that  all  the  corpuscles  which  strike  against  the 
metal  enter  it,  this  will  be  the  number'  of  corpuscles  entering 
the  metal,  and  therefore  in  the  steady  state  the  number  leaving  it  ; 
the  number  may  be  written  in  the  form 


this  number  multiplied  by  e  will  be  the  quantity  of  negative 
electricity  leaving  unit  area  of  the  metal  in  unit  time,  and 
therefore  will  be  the  saturation  current  from  a  hot  wire  at 
the  temperature  0,  Richardson's  measurements  of  the  saturation 
current  at  different  temperatures  '  agree  well,  as  we  have  seen, 
with  a  formula  of  this  form..  Ffrom  the  values  of  a  and  b  deter- 
mined by  experiments  on  the  escape  of  electricity  from  a  hot  wire 


168  IONISATION   BY   INCANDESCENT  SOLIDS.  [97 

we  can  deduce  the  values  of  N  and  w.     Richardson  found  that  for 
platinum 

a  =  T5  x  1026  and  6  =  4'93  x  104; 
this  gives 

N=  1-3  x  1021  and  w  =  8  x  10'12  ergs. 

The  pressure  due  to  the  corpuscles  in  the  metal  would  at  atmo- 
spheric temperature  be  between  30  and  40  atmospheres. 

97.  The  emission  of  the  negative  corpuscles  from  heated  sub- 
stances is  not,  I  think,  confined  to  the  solid  state,  but  is  a  property 
of  the  atom  in  whatever  state  of  physical  aggregation  it  may  occur, 
including  the  gaseous.  The  emission  of  the  negative  corpuscles 
from  the  atoms  is  well  shown  in  the  case  of  sodium  vapour ;  if 
a  little  sodium  be  placed  in  a  tube  from  which  all  gas  has  as  far 
as  possible  been  exhausted  there  will  be  in  the  dark  no  leak  from 
a  charged  conductor  sealed  in  the  tube,  if  however  the  tempera- 
ture is  raised  to  about  300°  C.  in  the  dark  a  considerable  leakage 
of  electricity  from  the  charged  conductor  will  occur,  whether  the 
charge  be  positive  or  negative ;  the  leak  in  the  former  case  is 
however  greater  than  in  the  latter.  It  might  be  thought  that 
the  leak  is  due  to  the  corpuscles  given  out  by  the  solid  sodium  in 
the  tube,  these  however  would  be  negatively  charged  and  could 
not  discharge  a  negatively  charged  conductor;  nor  is  it  due  to 
sodium  condensed  on  the  charged  conductor  itself,  for  there  is  no 
leak  on  cooling  down  to  the  temperature  of  the  room  and  ex- 
posing the  charged  conductor  when  negatively  electrified  to  light ; 
if  sodium  had  condensed  on  the  charged  metal  the  leak  would 
have  been  very  perceptible. 

The  emission  of  the  negatively  electrified  corpuscles  from 
sodium  atoms  is  conspicuous  as  it  occurs  at  an  exceptionally  low 
temperature ;  that  this  emission  occurs  in  other  cases  although  at 
very  much  higher  temperatures  is,  I  think,  shown  by  the  con- 
ductivity of  very  hot  gases  (or  at  any  rate  by  that  part  of  it  which 
is  not  due  to  ionisation  occurring  at  the  surface  of  glowing  metals), 
and  especially  by  the  very  high  velocity  possessed  by  the  negative 
ions  in  the  case  of  these  gases ;  the  emission  of  negatively  elec- 
trified corpuscles  from  atoms  at  a  very  high  temperature  is  thus 
a  property  of  a  very  large  number  of  elements,  possibly  of  all. 

The  emission  of  corpuscles  from  the  atom  must  play  a  very 


98]  IONISATION   BY    INCANDESCENT   SOLIDS.  169 

important  part  in  the  decomposition  of  the  molecules  of  a  com- 
pound by  heat,  if  the  forces  which  bind  the  atoms  together  in 
the  molecule  are  mainly  electrical  in  their  origin.  For  imagine 
a  molecule  consisting  of  two  atoms,  one,  A,  positively,  the  other,  B, 
negatively  electrified,  and  suppose  that  the  temperature  is  raised 
until  the  point  is  reached  when  the  negatively  electrified  atom 
begins  to  discharge  the  negatively  electrified  corpuscles:  when 
this  stage  is  reached  B  loses  a  corpuscle.  Let  us  suppose  that 
under  the  electric  field  this  corpuscle  finds  its  way  to  the  positively 
electrified  A  neutralising  its  charge,  so  that  momentarily  A  and  B 
are  without  charge,  the  attraction  previously  existing  between 
them  is  annulled  and  there  is  no  longer  anything  to  prevent  their 
drifting  apart.  It  does  not  follow  however  that  the  molecule  is 
necessarily  permanently  split  up,  for  A  has  now  no  positive  charge 
to  prevent  the  negative  corpuscles  from  escaping,  and  as  it  is  the 
electro-positive  element  in  the  compound  it  would  under  similar 
conditions  lose  corpuscles  more  readily  than  B;  thus  A  will  soon 
regain  its  positive  charge.  B  being  without  charge  cannot  dis- 
charge negative  corpuscles  as  easily  as  it  did  previously  when  it 
was  negatively  electrified,  thus  some  time  may  elapse  before  B 
emits  a  corpuscle,  and  in  the  interval  it  may  get  struck  by  a 
negative  corpuscle  and  thus  acquire  a  negative  charge,  recombina- 
tion might  then  occur  between  it  and  the  positively  charged  A, 
this  combination  being  dissolved  again  by  the  process  we  have 
already  sketched.  We  should  thus  get  to  a  state  in  which  there 
is  statistical  equilibrium,  the  number  of  recombinations  in  unit 
time  being  equal  to  the  number  of  atoms  dissociated  in  that  time : 
the  proportion  of  the  free  to  the  combined  atoms  will  depend  upon 
the  properties  of  each  of  the  atoms ;  the  more  easily  A  loses  its 
corpuscles  by  heating  and  the  greater  the  difficulty  of  getting 
the  corpuscles  out  of  B,  the  smaller  will  be  the  proportion  of  free 
atoms.  These  considerations  show  that  heat  may  produce  dis- 
sociation in  other  ways  than  the  more  commonly  recognised  one 
of  increasing  the  kinetic  energy  until  the  centrifugal  force  is  great 
enough  to  overpower  the  attraction. 

98.  We  thus  see  that  from  an  incandescent  wire  corpuscles  are 
projected  at  a  rate  sufficient  to  produce  a  very  large  rate  of  leak 
when  the  pressure  of  the  gas  surrounding  the  wire  is  very  low ; 
at  such  pressures  there  is  very  little  gas  to  hamper  the  motion  of 


170  IONISATION   BY   INCANDESCENT  SOLIDS.  [99 

the  corpuscles,  which  consequently  can  move  with  very  high 
velocities  ;  as  soon  as  a  corpuscle  emerges  from  the  incandescent 
surface  it  travels  away  from  it  towards  the  cylinder  surrounding 
the  wire,  and  when  the  current  between  the  wire  and  the  cylinder 
is  saturated  none  of  the  corpuscles  diffuse  back  again  into  the  wire. 

When  however  the  pressure  of  the  gas  surrounding  the  wire 
is  considerable  the  corpuscles  cannot  travel  so  freely,  they  tend  to 
accumulate  in  the  neighbourhood  of  the  wire  and  some  of  them 
diffuse  back  into  it  again.  The  density  of  the  corpuscles  in  the 
neighbourhood  of  the  wire  cannot  exceed  a  definite  value,  given 
by  equation  (3),  p.  166  :  just  as  in  the  case  of  the  evaporation  of 
a  liquid,  the  pressure  of  vapour  in  contact  with  the  liquid  cannot 
exceed  a  definite  value  depending  upon  the  temperature. 

99.  To  drive  through  a  gas  at  a  considerable  pressure  currents 
comparable  with  those  easily  obtainable  in  a  vacuum  would  re- 
quire the  application  of  very  large  differences  of  potential.  For 
let  us  take  the  case  of  two  parallel  plates  at  right  angles  to  the 
axis  of  x,  1  cm.  apart  ;  let  the  plate  x  =  0  be  the  hot  plate,  X  the 
electric  force  at  a  point  #,  u0  the  velocity  of  a  corpuscle  under 
unit  electric  force  ;  then  if  the  velocity  of  the  corpuscle  is  pro- 
portional to  the  electric  force,  the  velocity  at  the  point  x  will  be 
u0X,  and  if  n  be  the  number  of  corpuscles  per  unit  volume,  e  the 
charge  on  a  corpuscle,  i  the  current  through  unit  area,  then 
we  have 

i  =  u0Xne, 

dX 

— 

dx 

,  v  dX 

hence  X  —=— 


*  =        x  +     f, 
M0 

where  X0  is  the  value  of  X  at  the  surface  of  the  plate.  From  this 
equation  it  follows  that  if  V  is  the  potential  difference  between  the 
plate  and  a  point  x  away  from  it,  then 


F>    — 


99]  IONISATION   BY   INCANDESCENT   SOLIDS.  171 

From  this  expression  we  may  calculate  a  lower  limit  to  the 
potential  difference  necessary  to  send  a  current  of  1  milliampere 
per  square  centimetre  from  a  hot  to  a  cold  plate  1  cm.  distant 
when  the  gas  is  at  atmospheric  pressure ;  in  a  high  vacuum  and 
at  a  white  heat  such  a  current  could  be  produced  by  a  potential 
difference  of  100  volts  or  so.  In  order  to  get  a  lower  limit  for  V 
we  shall  give  to  u0  the  greatest  value  which  has  been  observed  for 
the  negative  ions  at  atmospheric  pressure ;  this  is  the  value 
obtained  by  H.  A.  Wilson  in  the  case  of  flames  at  a  temperature 
of  about  2000°  C.  and  is  equal  to  1000  cm. /sec.  for  a  potential 
gradient  of  1  volt  per  cm.  If  we  use  the  electrostatic  system 
of  units,  the  unit  electric  force  is  300  volts  per  cm. ;  hence 
for  the  case  quoted  u0  =  3  x  105cm./sec. :  on  the  same  system 
of  units  1  milliampere  =  3  x  106;  substituting  these  values  of 
i  and  u0  and  putting  a?=l,  we  find  V>  11  electrostatic  units  or 
3300  volts. 

From  these  results  we  see  that  if  the  emission  of  corpuscles 
was  the  only  effect  occurring  at  the  surface  of  the  wire  we  should 
at  high  pressures  get  a  small  leak  when  the  hot  wire  was  charged 
negatively,  no  leak  when  it  was  charged  positively.  There  would 
be  no  positive  leak  because  the  corpuscles  are  negatively  elec- 
trified, and  a  positive  leak  requires  a  supply  of  positive  ions. 
The  negative  corpuscles  when  moving  with  sufficient  velocity 
through  a  gas  ionise  it,  and  if  the  corpuscles  coming  from  the  wire 
moved  fast  enough  they  would  ionise  the  gas  around  the  wire,  and 
thus  produce  a  supply  of  positive  as  well  as  negative  ions;  the 
velocity  however  possessed  by  at  any  rate  an  enormous  majority  of 
the  ions  from  the  metal  is  far  too  small  to  produce  this  ionisation. 
When  the  field  is  so  intense  that  the  corpuscles  acquire  sufficient 
velocity  to  ionise  the  gas  the  current  will  increase  rapidly  with 
the  pressure. 

The  phenomena  we  have  already  described  show  that  when  gas 
is  present  there  must  be  other  sources  of  ionisation  besides  the 
corpuscles :  for  we  have  seen  that  beginning  at  a  very  dull  red 
heat  there  are  positive  ions  around  the  wire,  and  these  increase  as 
the  temperature  increases;  negative  ions  do  not  however  make 
their  appearance  until  about  a  bright  yellow  heat ;  they  increase 
more  rapidly  with  the  temperature  than  the  positive,  until  at  very 
high  temperatures  there  are  as  many  negative  as  positive  ;  indeed, 


172  IONISATION   BY   INCANDESCENT   SOLIDS.  [100 

in  the  opinion  of  Koch*,  the  number  of  the  negative  ions  at  these 
high  temperatures  exceeds  that  of  the  positive.  There  is  evidently 
some  source  of  ionisation  besides  the  emission  of  corpuscles  and 
one  which  begins  at  a  much  lower  temperature.  We  proceed  to 
the  consideration  of  some  of  the  effects  arising  from  it. 

100.  Incandescent  wire  surrounded  by  gas.  We  have  first  to 
notice  that  the  source  of  the  ionisation  is  at  the  surface  of  the 
incandescent  metal,  and  does  not  extend  to  any  considerable 
distance  in  the  gas.  One  proof  of  this  is  that  the  saturation 
current  between  an  incandescent  metal  plate  and  a  parallel  plate 
is  independent  of  the  distance  between  the  plates ;  thus  in  some 
experiments  I  made  on  this  point  I  found  that  the  saturation 
current  was  the  same  when  the  plates  were  3  mm.  apart  as  when 
they  were  5  mm.,  the  pressure  was  that  due  to  about  '25  mm.  of 
mercury ;  thus  even  at  this  low  pressure  the  source  of  ionisation 
did  not  extend  as  much  as  3  mm.  from  the  hot  plate,  for  if  it 
had  done  so  the  saturation  current  would  have  been  less  at  the 
smaller  distance. 

Another  very  striking  proof  of  the  same  thing  is  afforded  by 
the  experiments  of  H.  A.  Wilson  f  on  the  conductivity  of  flames 
containing  the  vapours  of  metallic  salts.  If  two  pieces  of  platinum 
foil  are  immersed  in  a  flame  so  as  to  be  heated  to  a  red  heat  and 
are  connected  with  the  terminals  of  a  galvanic  battery,  a  current 
will  pass  through  the  flame  from  one  of  these  electrodes  to  the 
other.  This  current  is  very  largely  increased  when  volatile  salts  are 
placed  in  the  flame  so  as  to  introduce  into  it  large  quantities  of 
salt  vapour.  Wilson  found  that  when  this  vapour  was  produced 
by  placing  a  small  bead  of  the  salt  in  the  flame  there  was  little 
or  no  increase  in  the  current  when  the  bead  was  so  placed  that 
the  vapour  did  not  come  into  contact  with  either  electrode;  when 
the  vapour  came  into  contact  with  the  positive  electrode  there 
was  a  substantial  increase  and  when  it  touched  the  negative 
electrode  a  very  large  one.  The  increase  in  the  current  produced 
by  the  vapour  indicates  an  increase  in  the  number  of  ions,  and 
the  preceding  results  show  that  this  increase  does  not  take  place 
unless  the  metallic  vapour  comes  into  contact  with  the  glowing 
metal. 

*  Koch,  Wied.  Ann.  xxxiii.  p.  454,  1888. 

f  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 


100] 


IONISATION   BY   INCANDESCENT   SOLIDS. 


173 


Another  proof  that  the  ionisation  is  confined  to  the  surface  of 
the  hot  metal  is  that  the  saturation  current  between  the  two 
electrodes  is  independent  of  their  distance  apart. 

We  can  by  the  following  method*  measure  the  conductivity  of 
a  flame  without  introducing  into  it  any  'metallic  electrodes  and 
can  thus  directly  determine  the  change  if  any  produced  in  the  case 
by  the  admixture  of  salt  vapours.  A  and  B  (Fig.  44)  are  two 


Fig.  44. 

Ley  den  jars  the  insides  of  which  are  connected  with  the  terminals 
of  an  induction  coil  or  electric  machine.  The  outside  coatings  of 
these  jars  are  connected  by  the  circuit  CDEF  containing  the  two 
loops  D  and  E ;  in  one  of  these  loops,  E,  a  glass  bulb  containing 
gas  at  a  very  low  pressure  is  placed :  when  the  coil  or  machine  is 
in  action  the  jars  are  continually  being  charged  and  discharged ; 
each  time  the  jars  are  discharged  alternating  currents  with,  for 
moderate  sized  jars,  a  frequency  of  some  millions  per  second  pass 
through  the  wire  CDEF',  the  currents  flowing  round  the  loop  E 
induce  currents  through  the  rarefied  gas  in  the  bulb,  these  currents 
through  the  gas  make  it  luminous,  so  that  the  discharge  of  the  jar 
is  accompanied  by  a  bright  ring  in  the  bulb  in  E.  If  conductors 
of  not  too  great  conductivity  are  inserted  in  the  loop  I)  it  will 
be  found  that  the  brightness  of  the  ring  in  E  is  diminished,  and 
the  higher  the  conductivity  the  greater  the  diminution;  in  this 
way  by  observing  the  effects  of  different  conductors  when  placed 
in  D  we  can  get  some  idea  of  their  conductivity.  Now  Wilson 
found  that  the  effect  of  the  flame  of  a  Bunsen  burner  passing 
through  D  upon  the  ring  discharge  in  E  was  quite  appreciable,  but 

*  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  viii.  p.  258,  1895. 


174-  IONISATION   BY   INCANDESCENT   SOLIDS.  [100 

that  this  effect  was  not  perceptibly  increased  when  salt  vapours  were 
introduced  into  the  flame  though  the  current  between  electrodes 
in  the  flame  was  increased  several  hundred  times  by  the  intro- 
duction of  the  salt. 

The  effect  of  a  conducting  metallic  plate  in  facilitating  ionisa- 
tion  in  its  neighbourhood  is  very  easily  explained  ;  ionisation 
involves  the  separation  of  a  positive  from  a  negative  charge  of 
electricity ;  if  these  charges  are  placed  close  to  a  metallic  plate, 
other  charges  will  be  induced  in  the  plate  which  will  almost  annul 
the  attraction  between  the  original  charges;  these  therefore  will 
be  much  more  easily  separated  than  when  they  are  far  from  con- 
ductors and  the  attraction  between  them  has  its  normal  value. 
The  strong  ionisation  of  salts  in  solvents  having  very  large  specific 
inductive  capacities  is  another  aspect  of  the  same  phenomenon, 
for  a  dielectric  of  high  inductive  capacity  produces  much  the  same 
kind  of  effect  on  the  attraction  between  electrical  charges  in  its 
neighbourhood  as  a  conductor:  it  thus  facilitates  the  separation 
of  the  charges  and  therefore  ionisation.  Water,  alcohol,  and  indeed 
all  ionising  solvents  have  large  specific  inductive  capacities. 

If  the  ionisation  is  confined  to  the  surface  of  the  incandescent 
metal,  then  the  current  between  a  hot  electrode  and  a  cold  one 
will  be  carried  by  ions  of  one  sign,  even  though  ions  of  both  signs 
are  found  at  the  surface  of  the  metal.  When  the  temperature  is 
so  low  that  only  ions  of  one  sign  are  produced  at  the  metal  (as  is 
the  case  with  platinum  below  a  yellow  heat),  then  all  the  ions 
carrying  the  current  must  have  come  from  the  same  electrode. 
This  explains  an  effect  observed  by  the  author  many  years  ago*: 
the  current  between  two  pieces  of  platinum  foil  immersed  in  a  vessel 
heated  to  a  bright  red  heat  was  found  to  be  completely  stopped  by 
placing  a  cold  metallic  plate  between  the  electrodes  and  the  current 
did  not  recommence  until  the  middle  plate  was  raised  to'  incan- 
descence. This  is  evidently  what  would  occur  if  there  was  a  pro- 
duction of  positive  ions  at  the  two  electrodes  A  and  B  and  nowhere 
else ;  for  suppose  A  is  the  positive  electrode,  then  all  the  ions 
which  reach  B  have  started  from  A ;  if  we  place  between  A  and  B 
a  plate  whether  made  of  a  conductor  or  insulator  we  stop  all  the 
ions  before  they  reach  B  and  thus  stop  the  current.  The  current 

*  J.  J.  Thomson,  Phil.  Mag.  v.  29,  p.  441,  1890. 


101]  IONISATION    BY   INCANDESCENT   SOLIDS.  175 

will  recommence  when  the  plate  gets  hot  enough  to  produce  ions 
at  its  surface.  If  ions  of  both  signs  are  produced  at  each  of  the 
hot  plates  the  current  will  not  be  stopped  by  the  middle  plate  but 
will  be  greatly  diminished. 

101.  Relation  between  the  current  and  the  potential  difference. 
Let  us  consider  the  case  of  two  parallel  plates  at  right  angles  to  the 
axis  of  a?,  then  if  only  one  of  the  plates  is  incandescent,  or  if  both 
are  incandescent  but  the  temperature  is  so  low  that  only  positive 
ions  are  produced  at  the  surface  of  the  plates,  then  the  ions 
carrying  the  current  between  the  plates  will  be  all  of  one  sign  and 
we  may  apply  the  results  of  Art.  98.  Hence  if  X  is  the  electric 
force,  R  the  velocity  of  the  ion  under  unit  electric  force,  we  have, 
if  i  is  the  current, 


_ 
dx~   R' 

hence  if  R  is  independent  of  x  we  have 


if  the  current  is  small  X  vanishes  at  the  hot  plate,  hence  if  the 
equation  to  this  plate  is  x  —  0, 


if  V  is  the  difference  of  potential  between  the  plates,  d  the  dis- 
tance apart,  we  have 


or 


.(1). 


This  equation  has  been  tested  by  Rutherford*;  we  canno4- 
however  expect  the  theory  to  be  in  very  close  agreement  with  the 
facts,  for  in  deducing  equation  (1)  we  have  made  several  assump- 
tions which  are  not  satisfied  in  practice;  in  the  first  place  we 
have  assumed  that  R  is  independent  of  x,  this  will  only  be  true 
when  the  temperature  is  uniform  between  the  plates,  it  will  not 
be  true  when  one  plate  is  hot  and  the  other  cold,  for  the  velocity 

*  Rutherford,  Physical  Review,  xiii.  p.  321,  1901. 


176  ION1SATION   BY   INCANDESCENT   SOLIDS.  [101 

of  the  ion  depends  upon  the  temperature.  Thus  H.  A.  Wilson*  has 
shown  that  in  a  flame  at  the  temperature  of  about  2000°  C.  the 
velocity  of  the  negative  ion  under  a  potential  gradient  of  1  volt 
per  cm.  is  about  1000  cm. /sec.,  that  of  the  positive  ion  under  the 
same  gradient  62  cm. /sec.;  in  hot  air  at  a  temperature  of  about 
1000°  C.  the  velocity  of  the  negative  ion  is  only  about  26  cm./sec., 
that  of  the  positive  about  7*2  cm./sec.  McClelland-f-  found  that  the 
ions  from  an  incandescent  wire  when  they  got  into  the  cold  air  at 
some  distance  from  the  wire  travelled  with  velocities  as  small  as 
'04  cm./sec.:  and  that  the  velocity  diminished  as  the  ions  got  further 
from  the  wire  and  could  be  increased  again  by  warming  the  ions ; 
thus  R  varies  rapidly  with  the  temperature  and  therefore  with  x. 

The  increase  of  R  with  the  temperature  makes  the  current 
increase  rapidly  with  the  temperature  of  the  hot  plate.  We 
see  from  equation  (1)  that  the  current  for  a  constant  small 
difference  of  potential  does  not  depend  upon  the  amount  of  ioni- 
sation  near  the  plate  j,  so  that  the  increase  of  ionisation  at  the 
higher  temperature  would  not  explain  the  increase  of  current  when 
the  wire  gets  hotter ;  a  satisfactory  explanation  of  this  increase  is 
however  afforded  by  the  increase  of  R  with  the  temperature. 

WThen  the  temperature  of  the  hot  plate  is  high  enough  for 
negative  as  well  as  positive  ions  to  exist  near  the  plate,  the 
leak  between  the  hot  plate  and  a  cold  one  will  be  greater  when 
the  hot  plate  is  the  negative  electrode  than  when  it  is  the  positive : 
for  in  the  former  case  the  current  is  carried  by  negative  ions,  in 
the  latter  by  positive,  and  equation  (1)  shows  that  with  the  same 
potential  difference  the  current  is  proportional  to  the  velocity  of 
the  ion  by  which  it  is  carried.  Now  the  velocity  of  the  negative 
ion  is  always  greater  than  that  of  the  positive,  and  the  ratio  of  the 
velocity  of  the  negative  to  that  of  the  positive  increases  rapidly 
with  the  temperature;  thus  the  experiments  of  H.  A.  Wilson  on 
the  leak  through  gases  mixed  with  the  vapours  of  salt  (I.e.}  show 
that  this  ratio  at  2000°  C.  is  about  17  while  at  1000°  C.  it  is  only 
about  3 '5.  At  ordinary  temperatures  for  the  case  of  ions  drawn 

*  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 

f  McClelland,  Phil.  Mag.  v.  46,  p.  29,  1899. 

I  It  must  be  remembered  that  equation  (1)  only  applies  when  the  current  is 
small,  so  that  X=0  when  x  =  0-,  when  the  current  approaches  saturation  it  increases 
rapidly  with  the  amount  of  ionisation  at  the  plate. 


102] 


IONISATION   BY   INCANDESCENT   SOLIDS. 


177 


from  the  neighbourhood  of  the  hot  wire,  McClelland's  experiments 
show  that  this  ratio  is  only  about  1'25.  The  great  increase  of 
current  produced  by  changing  the  sign  of  a  very  hot  electrode 
from  +  to  —  is  a  very  well  marked  phenomenon;  one  striking 
example  of  it  is  furnished  by  an  old  experiment  of  Hittorf's  *.  In 
this  experiment  a  bead  of  salt  was  placed  in  a  flame  between 
glowing  electrodes :  the  increase  in  the  current  was  much 
greater  when  the  bead  was  placed  close  to  the  negative  electrode 
than  when  it  was  placed  near  to  the  positive.  These  results,  it 
must  be  remembered,  are  only  true  when  the  currents  are  very 
small  compared  with  their  saturation  values;  the  saturation  values 
do  not  depend  upon  the  velocities  of  the  ions  but  only  upon  the 
number  of  ions  produced  in  unit  time  at  the  surface  of  the  hot 
metal. 

The  velocity  of  an  ion  under  a  constant  electric  force  increases 
as  the  pressure  of  the  gas  diminishes,  hence  we  see  from  equation 
(1)  that  the  current  when  small  will  increase  when  the  pressure 
diminishes. 


100 


200 


300 


Fig.  45. 


400  Cells 
(=800  Volts) 


102.    A  well-marked  feature  of  the  discharge  from  incandescent 
metals  is  the  very  rapid  increase  of  the  current,  when  this  is  small, 


*  Hittorf,  Fogg.  Ann.  Jubelband,  p.  430,  1874. 


T.  G. 


12 


178  IONISATION   BY   INCANDESCENT  SOLIDS.  [103 

with  the  electromotive  force,  an  increase  much  more  rapid  than 
that  given  by  Ohm's  law.  This  has  frequently  been  observed ;  thus, 
for  example,  Pringsheim  *  gives  as  an  empirical  formula  for  the 
current  i  in  terms  of  the  potential  difference  V  for  the  discharge 
between  two  pointed  electrodes  in  a  hot  gas 

._F+aF2 
~1T~' 

where  a  and  w  are  constants.  The  rapid  increase  in  the  current  is 
well  illustrated  by  the  curve  in  Fig.  45  given  by  H.  A.  Wilson + 
for  the  case  of  the  current  between  a  hot  platinum  wire  and  a  hot 
platinum  tube  outside  it;  in  this  curve  the  ordinates  represent 
the  current  and  the  abscissse  the  potential  differences,  the  curve 
for  the  case  when  the  tube  is  negative  illustrates  too  the  '  satura- 
tion '  of  the  current  under  high  electromotive  forces.  This  rapid 
increase  of  the  current  is  accounted  for  by  equation  (1),  which 
shows  that  the  current  is  proportional  to  the  square  of  the 
potential  difference. 

103.  The  nature  of  the  carriers  of  the  electricity  in  the  current 
from  a  hot  wire.  The  discharge  of  positive  electricity  from  a  wire 
at  a  temperature  between  a  red  and  yellow  heat  is  not  determined 
solely  by  the  nature  and  pressure  of  the  gas  and  the  temperature 
of  the  wire,  it  is  very  largely  influenced  by  the  treatment  to  which 
the  wire  has  been  subjected  previous  to  the  discharge.  Thus  if  we 
measure  the  leak  between  a  hot  wire  and  a  cold  metal  cylinder 
surrounding  it,  the  gas  being  at  a  low  pressure,  we  often  find  that 
when  the  wire  is  first  heated  the  leak  is  very  large  to  begin  with, 
but  slowly  diminishes  until  after  several  hours'  continuous  heating 
the  current  may  have  sunk  to  1/20  of  its  original  value  :  if  when 
it  has  fallen  to  this  point  fresh  gas  is  introduced  into  the  vessel 
containing  the  hot  wire  and  then  after  some  time  pumped  out 
until  the  pressure  is  the  same  as  before  the  introduction  of  the 
gas,  the  current  is  very  greatly  increased  for  a  time ;  it  again 
diminishes  as  the  heating  continues  but  can  be  revived  by  the 
introduction  of  fresh  gas.  As  this  diminution  occurs  whether  or 
not  the  current  is  kept  flowing  between  the  hot  wire  and  the  sur- 
rounding cylinder,  it  cannot  be  due  to  an  effect  analogous  to  the 

*  Pringsheim,  Wied.  Ann.  Iv.  p.  507,  1895. 

t  H.  A.  Wilson,  Phil.  Trans.  A.  197,  p.  415,  1901. 


103]  IONISATION    BY   INCANDESCENT   SOLIDS.  179 

ordinary  polarisation  of  electrolytes,  although  we  shall  see  reasons 
for  thinking  that  such  an  effect  does  exist  to  some  extent  in 
conduction  through  hot  gases. 

The  facts  just  mentioned  suggest  that  the  gas  absorbed  by  the 
platinum  and  slowly  given  off  when  heated  plays  an  important 
part  in  the  carriage  of  the  electricity  from  the  wire,  and  we  can 
easily  understand  how  this  gas,  coining  straight  from  the  midst  of 
a  good  conductor,  would  be  ionised  and  able  to  carry  the  current. 
The  emission  of  absorbed  gas  from  the  platinum  is  however, 
according  to  Berliner*,  closely  connected  with  the  disintegration 
of  the  platinum  wire  which  takes  place  when  the  wire  is  kept 
glowing  and  which  is  made  evident  by  a  deposit  of  platinum  or 
platinum  oxide  on  the  walls  of  the  tube  and  a  diminution  in  the 
weight  of  the  hot  wire :  the  carriers  of  the  electricity  might  thus 
be  the  dust  or  vapour  of  platinum  escaping  from  the  wire.  This 
disintegration  of  the  platinum  has  been  studied  by  Berliner*, 
Elster  and  Geitel  f,  Nahrwold  },  and  Stewart  § :  who  have  shown 

(1)  That  the  amount  of  disintegration  produced  in  a  given 
time  by  the  incandescence  of  a  platinum  wire  diminishes  after 
prolonged  heating. 

(2)  That  the  amount  of  this  disintegration  is  very  much  in- 
creased by  the  presence  of  oxygen.     It  is  exceedingly  small  in 
nitrogen  and  hydrogen ;  indeed,  some  of  the  experiments  suggest 
that  there  would  be  no  disintegration  of  a  glowing  platinum  wire 
in  these  gases  if  every  trace  of  oxygen  could  be  removed  from 
them.     We  may  suppose  that  where  oxygen  is  present  slight 
oxidation   takes  place,  producing   a  weathering   of  the   surface 
which  facilitates  the  disintegration  of  the  metal. 

The  disintegration  of  the  platinum  can  be  easily  shown  by 
the  effect  of  the  incandescence  of  the  wire  on  the  condensatio: 
of  clouds  in  the  air  in  its  neighbourhood.     We  owe  this  method 
to  Aitken||.     One  simple  way  of  showing  this  effect  is  to  have 
a  fine  platinum  wire  fused  in  the  expansion  chamber  in  the  cloud 

*  Berliner,  Wied.  Ann.  xxxiii.  p.  289,  1888;  xxxv.  p.  791,  1888. 

t  Elster  and  Geitel,  Wied.  Ann.  xxxi.  p.  109,  1887. 

t  Nahrwold,  Wied.  Ann.  xxxi.  p.  448,  1887;  xxxv.  p.  107,  1888. 

§  Stewart,  Phil.  Mag.  xlviii.  p.  481,  1889. 

||  Aitken,  Trans.  Roy.  Soc.  Edin.  xxx.  p.  337. 

12—2 


180  IONISATION   BY   INCANDESCENT   SOLIDS.  [104 

apparatus  (Fig.  37).  If  the  air  be  made  dust-free  when  the  wire 
is  cold,  then  on  sending  a  current  through  the  wire  so  as  to  raise 
it  to  a  red  heat  and  then  letting  it  cool,  a  dense  cloud  is  produced 
by  a  very  small  expansion;  as  this  expansion  is  much  smaller  than 
that  required  to  produce  a  cloud  on  ions,  there  must  be  particles 
much  larger  than  molecules  in  the  neighbourhood  of  the  wire. 
Unless  the  wire  is  very  carefully  cleaned  an  increase  of  tem- 
perature much  less  than  that  required  to  produce  luminosity  is 
sufficient  to  produce  a  cloud.  This  depends  apparently  upon  dirt 
or  moisture  deposited  on  the  wire,  and  Aitken's  experiments 
show  that  this  effect  disappears  when  the  wire  has  been  cleaned 
by  long-continued  incandescence ;  no  amount  of  incandescence 
seems  however  to  destroy  the  cloud  when  the  temperature  of 
the  platinum  wire  is  raised  to  that  corresponding  to  a  red  heat. 
Mr  Owen,  who  has  recently  made  experiments  in  the  Cavendish 
Laboratory  on  this  point,  finds  that  when  the  platinum  wire  is  in 
air  or  oxygen  there  is,  even  after  long-continued  incandescence  of 
the  wire,  always  a  cloud  when  the  temperature  of  the  wire  is  raised 
to  about  300°  C.  In  pure  hydrogen  however  the  wire  has  to  be 
raised  nearly  to  a  red  heat  before  this  cloud  is  formed. 

104.  There  is  a  close  similarity  between  the  laws  of  disintegra- 
tion of  the  wire  and  those  of  the  leak  of  positive  electricity  from  it. 
We  have  already  alluded  to  the  effect  of  long-continued  heating 
on  the  leak  :  the  presence  of  oxygen  has  also  a  very  marked  effect. 
This  can  be  shown  in  a  striking  way  by  observing  the  pressure 
at  which  a  plate  in  the  neighbourhood  of  the  hot  wire  begins 
to  acquire  a  negative  instead  of  a  positive  charge.  If  the  wire 
^be  not  too  hot,  then  at  high  pressures  the  plate  will  be  charged 
positively  ;  on  exhausting  the  vessel  a  point  will  be  reached  where 
the  positive  charge  begins  to  decrease,  then  vanishes  and  finally 
is  replaced  by  a  negative  charge.  This  change  in  the  sign  of  the 
charge  on  the  plate  occurs  at  much  higher  pressures  in  hydrogen 
and  nitrogen  than  in  oxygen,  where  this  reversal  is  difficult  to 
obtain  unless  the  wire  be  very  hot.  When  the  reversal  of  sign 
has  been  obtained  in  hydrogen  or  nitrogen  the  addition  of  a 
surprisingly  small  quantity  of  oxygen  is  sufficient  to  make  the 
charge  on  the  plate  positive  again.  It  is  possible  that  part  of 
the  diminution  in  the  positive  leak  produced  by  long-continued 
heating  at  low  pressures  may  be  due  to  the  burning  up  of  the 


105]  IONISATION   BY    INCANDESCENT   SOLIDS.  181 

oxygen,  or  when  there  is  any  grease  present  to  the  replacement 
of  oxygen  by  the  vapours  of  hydrocarbons  liberated  by  the  con- 
tinuous heating.  The  increase  in  the  positive  electrification 
produced  by  oxygen  is  easily  explained  if  there  is  any  oxidation 
of  the  metal  at  a  red  heat ;  for  in  the  oxide  thus  formed  the 
oxygen  carries  the  negative,  the  metal  the  positive  charge;  thus 
if  the  oxygen  in  the  neighbourhood  of  the  platinum  wire  got 
ionised  by  the  heat,  the  platinum  by  combining  with  the  negative 
but  not  with  the  positive  oxygen  ions  would  leave  an  excess  of 
positive  ions  in  the  neighbourhood.  That  chemical  action  has 
a  considerable  effect  on  the  electrification  is  confirmed  by  the 
observation  of  Branly  that  the  oxides  of  metals  give  off  at  a  dull 
red  heat  negative  electricity,  whereas  metals  give  off  positive ;  in 
the  case  of  the  oxides  the  chemical  action  which  takes  place  is  the 
dissociation  of  the  oxide  into  the  metal  and  oxygen,  the  oxygen 
ions  carrying  the  negative  charge  and  thus  producing  negative 
electrification  round  the  wire.  A  similar  explanation  applies  to 
the  following  result  which  I  observed  with  the  arc  discharge ; 
when  the  arc  passed  between  terminals  of  bright  copper  there 
was  an  excess  of  positive  electricity  in  the  gas  round  the  ter- 
minals ;  if  however  the  terminals  were  thickly  coated  with  oxide 
and  placed  in  hydrogen  the  electrification  in  the  gas  was  negative 
until  the  oxide  was  reduced :  when  this  had  been  accomplished 
the  electrification  became  positive. 

105.  A  very  small  amount  of  chemical  action  is  sufficient  to 
produce  very  intense  electrification,  so  that  it  might  be  urged  that 
even  in  the  best  attainable  vacuum  there  is  sufficient  gas  to  produce 
the  electrification ;  that  this  positive  electrification  occurs  in  very 
good  vacua  is  certain ;  in  a  vacuum  so  good  that  it  was  hardly 
possible  to  get  any  discharge  through  it  with  an  induction  coil 
giving  an  8-iiich  spark,  I  have  got  the  positive  electrification 
from  a  red-hot  platinum  wire  which  had  been  kept  glowing  at 
a  much  higher  temperature  8  hours  a  day  for  a  week.  Stronger 
evidence  that  the  positive  electrification  is  not  due  entirely  to 
chemical  action  on  the  wire  is  afforded  by  a  determination  of  the 
nature  of  the  carriers  of  this  charge ;  if  the  charge  arose  from 
chemical  action  we  should  expect  the  carriers  to  be  the  atoms 
or  molecules  of  the  gas.  The  following  experiments  show  that 
although  there  are  a  few  carriers  of  this  character  the  majority 


182  IONISATION   BY   INCANDESCENT  SOLIDS.  [105 

of  them  are  much  larger  and  are  probably  molecules,  ,or  even 
larger  masses,  of  platinum.  The  method  used  to  determine  the 
mass  of  the  carriers  was  the  same  as  that  used  (see  p.  106)  to 
determine  the  mass  of  the  negative  carriers  at  high  temperatures, 
inasmuch  however  as  the  mass  of  the  positive  carriers  turns  out 
to  be  enormously  greater  than  that  of  the  negative  ones,  it  is 
necessary  in  dealing  with  the  positive  leak  to  employ  very  much 
greater  magnetic  forces  than  those  used  in  the  previous  ex- 
periments, and  this  involves  some  modifications  in  the  conditions 
of  the  experiment.  The  arrangement  used  is  shown  in  Fig.  46. 


To  Electrometer 


Battery 


Fig.  46. 

A  is  an  insulated  metal  plate  placed  in  the  middle  of  a  brass 
tube  about  5  mm.  in  diameter;  this  plate  is  connected  with  a 
quadrant  electrometer.  B  is  a  piece  of  platinum  foil  parallel  to 
the  plate  and  about  3  mm.  from  it ;  this  foil  can  be  raised  to 
incandescence  by  an  alternating  electric  current  passing  through 
the  leads  C,  D.  The  current  was  produced  by  making  the  circuit 
connecting  the  leads  loop  round  a  transformer.  By  this  method 
the  hot  wire  and  its  leads  could  be  easily  insulated  i  the  hot  wire 
and  the  brass  tube  were  connected  with  one  terminal  of  a  battery 
of  small  storage  cells,  the  other  terminal  of  which  was  connected 
with  the  earth.  The  current  to  the  plate  A  from  the  hot  wire  was 
measured  by  the  deflection  produced  in  the  electrometer  in  a  given 
time;  this  deflection  was  measured  for  various  potentials  of  the  hot 
wire,  with  the  magnetic  field  both  on  and  off ;  the  highest  potential 
at  which  a  given  magnetic  field  produces  an  appreciable  diminu- 
tion gives,  as  is  explained  in  Art.  48,  the  means  of  determining 


105]  IONISATION   BY   INCANDESCENT  SOLIDS.  183 

m/e  —  the  ratio  of  the  mass  of  the  carrier  to  its  charge.  In  the 
investigation  of  Art.  48  it  was  assumed  that  the  electric  force 
was  uniform  in  the  region  in  which  the  ions  were  moving;  in  the 
case  of  the  hot  wire  there  are  so  many  ions  all  of  one  sign 
carrying  the  current  that  they  disturb  the  potential  gradient 
and  make  the  force  vary  from  point  to  point.  We  can  easily 
prove  however  that  this  inequality  in  the  electric  field  will  not 
impair  the  validity  of  the  method.  If  the  field  is  not  uniform 
the  paths  of  the  ions  will  not  be  cycloids  ;  the  ions  however 
whether  the  field  is  uniform  or  not,  after  receding  a  certain 
distance  d  from  their  source,  will  be  turned  round  by  the  mag- 
netic force  and  begin  to  move  back,  thus  they  will  never  get 
further  than  d  away  from  the  source.  Now  if  the  plate  on  which 
the  ions  are  received  is  at  a  distance  greater  than  d  from  the  hot 
metal  which  is  the  source  of  the  ions,  the  magnetic  field  will 
produce  a  diminution  in  the  current  flowing  into  the  plate,  while 
if  the  distance  is  less  than  d,  the  magnetic  field  will  produce  no 
diminution  in  the  leak.  This  critical  distance  d  can  be  de- 
termined by  comparing  the  currents  with  the  magnetic  field  on 
and  off:  it  is  evidently  the  distance  from  the  source  at  which 
the  velocity  of  the  ion  parallel  to  the  electric  force  vanishes. 
If  x  is  the  distance  of  an  ion  from  the  hot  plate,  X  the  electric 
force  acting  on  the  ion,  H  the  magnetic  force  supposed  to  be 
uniform  and  parallel  to  the  axis  of  z,  then  we  have 
d*x  ~  TT  dy 


<2> 


or  m-£  =  -  Hex, 

at 

since    -j-  =  0,    when   x  =  0 ;   substituting   this   value   for   -j-  ;n 
at  ut 

equation  (1)  we  get 

r/'2r       TfV2 

LV      W  i  1~        &  -TT- 

m  -jrt  +  -    -  x  =  A  e. 
ar        m 

Integrating  with  respect  to  x  from  a?  =  0  to  x  =  d,  we  have  since 
(&e/<ft  vanishes  both  when  x  =  0  and  when  a?  =  d 

£  -        --  =  e  \    Xdx ; 
m  Jo 


184  IONISATION   BY   INCANDESCENT  SOLIDS.  [105 

if  V  is  the  difference  of  potential  between  the  plates  V — 

Jo 

hence  \ d*  =  V 

m 


e       2V 
= 


and  thus  even  when  the  field  is  not  uniform  e/m  is  given  by  the 
same  equation  as  in  Art.  48. 

In  applying  this  method  to  the  case  of  the  leaking  of  positive 
electricity  from  a  hot  wire  we  find  that  enormously  greater  mag- 
netic forces  are  necessary  to  produce  any  diminution  upon  the  leak 
than  were  required  to  produce  the  same  effect  on  the  leak  of 
negative  electricity  from  a  hot  wire  (see  p.  164):  and  even  with 
the  greatest  magnetic  forces  obtainable  the  effects  of  the  magnetic 
field  upon  the  rate  of  leak  are  sometimes  scarcely  appreciable. 
The  effect  of  a  magnetic  field  upon  the  positive  leak  like  the 
positive  leak  itself  is  irregular,  even  when  the  temperature  of  the 
wire  and  the  pressure  of  the  gas  are  kept  as  constant  as  possible, 
small  changes  in  conditions  which  it  is  very  difficult  to  control  or 
even  to  specify  producing  great  changes  in  the  leak  and  in  the 
effect  of  the  magnetic  field  upon  it.  It  is  probable  that  these 
changes  correspond  to  a  change  in  the  nature  of  the  carriers  of 
the  electricity.  In  some  cases  the  leak  is  not  affected  by  the 
magnetic  field  even  of  19000  units.  When,  however,  the  discharge 
is  sensitive  to  the  magnetic  field  the  general  nature  of  the  effects 
observed  with  the  apparatus  already  described  and  with  a  field 
of  19000  units  is  as  follows,  the  pressure  of  the  gas  (air)  being 
about  '007  mm.  ;  the  numbers  given  are  only  approximate  as  the 
irregular  variations  in  the  leak  are  so  large  as  to  make  accurate 
measurement  impossible.  When  the  potential  difference  between 
the  hot  metal  and  the  plate  connected  with  the  electrometer  was 
small,  say  3  or  4  volts,  the  leak  was  very  nearly  stopped  by  the 
magnetic  field;  with  a  potential  difference  of  10  volts  the  leak  was 
reduced  by  the  magnetic  field  to  about  one-quarter  of  its  original 
value,  the  effect  of  the  magnetic  force  upon  the  leak  diminished  as 
the  potential  difference  increased  but  was  appreciable  until  this 
reached  about  120  volts.  Thus  in  this  case  we  see  that  while  some 
of  the  carriers  can  reach  the  plate  under  a  difference  of  potential 
of  10  volts,  there  are  others  which  require  a  potential  difference 


105]  IONISATION   BY    INCANDESCENT   SOLIDS.  185 

of  120  volts  to  do  so.  If  e1/m1  be  the  ratio  of  the  charge  to  the 
mass  of  the  first  carrier,  e2/m2  that  of  the  second,  then  putting 
in  equation  (8) 

H=  19000,  d  =  -3  and  F=  10  x  108  and  120  x  108,  we  get 


m 


2  =720; 
m2 

if  elt  e*  were  the  same  as  the  charge  on  a  hydrogen  ion,  then  77^ 
and  w2  would  be  respectively  about  170  and  14  times  the  mass  of 
the  hydrogen  atom;  these  are  limiting  values  of  e/mt  there  are  also 
intermediate  values.  These  results  indicate  that  the  electricity  is 
carried  both  by  atoms  of  the  metal  (in  this  case  platinum)  and  of 
the  gas,  the  former  predominating.  The  fact  that  in  certain  cases 
the  rate  of  leak  is  not  affected  by  the  magnetic  force  even  when 
the  potential  difference  is  reduced  to  one  volt  or  less  shows  that  in 
these  cases  the  carriers  have  much  larger  mass  than  the  molecule 
of  platinum,  they  are  probably  platinum  dust. 

Rutherford*  from  experiments  on  the  velocity  of  the  ions 
through  air  at  atmospheric  pressure  also  came  to  the  conclusion 
that  carriers  of  very  different  kinds  were  at  work  in  carrying  the 
positive  electricity  from  a  hot  metal. 

Though  the  effect  of  the  magnetic  field  on  the  rate  of  leak 
diminishes  when  the  potential  difference  is  increased  and  at  one 
stage  disappears,  yet  on  still  further  increasing  the  potential  a 
stage  is  reached  where  the  magnetic  force  again  produces  a  very 
considerable  diminution  in  the  rate  of  leak.  This  stage  is  closely 
connected  with  the  way  in  which  the  rate  of  leak  varies  with 
potential  difference  ;  if  we  represent  the  rate  of  leak  by  the  ordi- 
nates,  the  potential  difference  by  the  abscissae  of  a  point  on  a  curve, 
then  as  McClellandf  has  shown,  the  curve  is  of  the  type  represented 
in  Fig.  47  showing  three  well-marked  stages  :  in  the  first  the 
current  increases  rapidly  with  the  potential  difference,  in  the 
second  the  current  is  saturated  and  is  independent  of  the  potential 
difference,  in  the  third  stage  the  current  again  increases  rapidly. 
This  increase  is  as  we  shall  see  due  to  the  formation  of  fresh  ions 
by  the  motion  through  the  gas  of  ions  coming  from  the  hot  plate, 

*  Rutherford,  Physical  Review,  xiii.  p.  321,  1901. 
t  McClelland,  Proc.  Camb.  Phil.  Soc.  xi.  p.  296,  1902. 


186 


ION1SATION   BY   INCANDESCENT   SOLIDS. 


[105 


there  are  in  this  stage  negative  as  well  as  positive  ions  between 
the  electrodes.     It  is  in  the  third  stage  that  the  magnetic  field 


• 

2 

/ 

/ 

/ 

7 

X 

/ 

_—  —  -* 

e—  —  •  " 

^ 

y* 

^ 

D 

4 

0 

8 

0 

12 

0 

1C 

0 

Fig 

2 

.  47 

DO 

2< 

10 

2! 

JO 

32 

0 

36 

again  produces  a  diminution  in  the  rate  of  leak,  the  explanation 
of  this  is  I  think  that  the  magnet  stops  the  motion  of  the  negative 
ions  which  are  now  helping  to  carry  the  current  and  which  as  we 
have  seen  are  very  much  hampered  by  a  magnetic  field. 

Elster  and  Geitel*  found  that  the  rate  of  positive  leak  was  often, 
indeed  in  their  experiments  generally,  increased,  not  diminished, 
by  the  magnetic  field ;  with  the  apparatus  described  and  arranged 
as  on  page  182,  I  only  observed  an  increase  in  one  case,  i.e. 
when  the  temperature  was  high  and  the  potential  difference  small. 
At  a  very  high  temperature  negative  as  well  as  positive  ions  are 
produced  at  the  plate,  these  negative  ions  are  projected  with  great 
velocity  so  that  even  if  the  plate  has  a  small  positive  charge  the 
negative  ions  coming  from  the  plate  will  exceed  the  positive  ones 
and  a  conductor  in  the  neighbourhood  will  receive  a  negative 
charge.  If  the  potential  of  the  plate  be  raised  until  this  conductor 
gets  a  positive  charge,  then  the  application  of  a  magnetic  field  will 
often  considerably  increase  the  positive  charge  on  the  conductor ; 
this  increase  is,  however,  due  to  the  retardation  of  the  stream  of 
negative  ions  and  not  to  the  acceleration  of  the  positive  ones.  If 
the  metal  tube  in  which  the  hot  plate  (Fig.  46)  is  contained  is 
not  connected  with  the  hot  plate  but  with  the  earth,  then  a  mag- 
netic field  will  often  increase  the  rate  at  which  the  plate  acquires 
a  positive  charge;  this,  however,  is  merely  the  diversion  of  positive 
ions  from  the  tube  to  the  cold  plate  by  the  magnetic  field. 
*  Elster  and  Geitel,  Wied.  Ann.  xxxviii.  p.  27,  1889. 


106]  IONISATION    BY    INCANDESCENT   SOLIDS.  187 

106.  We  could  determine  the  value  of  e/m  for  the  carriers  of 
electricity  by  the  following  method,  which  is  applicable  when  the 
current  is  carried  by  ions  of  one  sign  and  when  the  pressure  of 
the  gas  is  so  low  that  we  can  neglect  the  resistance  of  the  gas  to 
the  motion  of  the  ions.  Let  us  consider  the  case  of  a  current 
between  two  parallel  plates,  one  of  which  is  the  hot  plate  or  other 
source  of  ions.  Take  the  axis  of  x  at  right  angles  to  the  plate,  let 
F  be  the  difference  of  potential  between  the  hot  plate  and  a  point 
whose  coordinate  is  x,  p  the  density  of  the  electricity.  Then 


If  v  be  the  velocity  of  the  ion  at  x,  VQ  its  velocity  when  starting 
from  the  plate,  m  its  mass  and  e  its  charge,  then 

±m(v2-v0*)  =  Ve    .....................  (2); 

but  since  all  the  ions  are  of  one  sign,  i  the  current  through  unit 
area  is  equal  to  vp,  hence  from  (1)  and  (2) 


m        '  *  "~*  '  ' 


integrating  this  equation  we  have,  if  we  write  X  for  dVjdx, 


=c 


+ 


e        (         m 

hence  if  X  is  the  value  at  the  cold  plate,  XQ  that  at  the  hot,  F  the 
potential  difference  between  the  plates,  and  C  the  constant  of 
integration, 

we  have  X*  —  X(?  •• 


if  X'  and  X0't  i'  and   V  are  corresponding  values  in  a  second 
experiment  we  have 

Z/2-Z/sl  =  8— —  rV+-F'j'-^l  ' 
«         LI  °       m       )          J  ' 

hence  if         (Z2  -  X02)/87ri  =  £     (Z/2  -  Z0/2)/87riv  =  £' , 

we  have  ^  f2  +  2^0  -  f  =  —  F, 

m  mm 


^£'t+2v0-?  =  - 
m*  •  m*       m 


(4), 


188  IONISATION    BY    INCANDESCENT   SOLIDS.  [107 

an  equation  by  which  we  can  determine  e/m  when  we  know 
f ,  f ',  V,  and  V.  To  determine  f  and  f '  we  require  to  know  the 
value  of  X  at  the  two  plates.  This  can  be  done  as  follows :  as 
the  pressure  is  very  low  we  can  produce  by  independent  electrodes 
cathode  rays  in  the  vessel  in  which  the  leak  is  taking  place;  if  we 
arrange  these  electrodes  so  ns  to  allow  a  small  pencil  of  these  rays 
to  pass  close  to  first  one  plate  and  then  the  other  and  measure 
the  electrostatic  deflection  of  the  rays,  we  can  from  this  deflection 
deduce  the  electric  force  and  then  by  equation  (4)  the  value  of 
e/m. 

Effect  of  the  Gas  on  the  rate  of  leak. 

107.  We  have  seen  that  in  the  best  vacua  we  can  produce  a 
metal  when  first  it  begins  to  glow  gives  oflf  positive  electricity 
and  then  at  considerably  higher  temperatures  negative  electricity 
as  well,  the  rate  of  emission  of  negative  electricity  increasing  more 
rapidly  with  the  temperature  than  that  of  the  positive,  so  that  at 
very  high  temperatures  the  negative  is  greatly  in  excess  of  the 
positive.  Thus  to  make  a  metal  emit  positive  electricity  we  have 
to  communicate  a  certain  amount  of  energy  to  its  surface,  a  larger 
amount  being  required  to  make  it  give  out  negative  electricity. 
When  the  incandescent  metal  is  surrounded  by  gas  at  an  appre- 
ciable pressure  we  find  that  the  nature  of  the  gas  has  a  very 
distinct  effect  upon  the  amount  of  leak.  The  author*  has  shown 
that  gases  such  as  the  vapours  of  iodine  and  bromine,  chlorine, 
hydriodic  acid  gas,  hydrobromic  acid  gas,  hydrochloric  acid  gas, 
the  vapours  of  potassium  iodide,  sal-ammoniac,  sodium  chloride, 
potassium  chloride,  which  are  dissociated  by  heat  conduct  elec- 
tricity on  quite  a  different  scale  from  those  which  like  air, 
hydrogen  or  nitrogen  do  not  suffer  any  dissociation ;  thus  the 
dissociable  gases  furnish  a  much  larger  supply  of  ions  than  the 
others :  even  in  these  easily  dissociable  gases  by  far  the  greater 
part  of  the  dissociation  occurs  where  the  gas  is  in  contact  with  the 
glowing  electrodes ;  this  is  proved  by  the  experiment  described  on 
page  172. 

The  vapours  of  many  metals  conduct  very  well ;  of  the  metals  I 
tried,  sodium,  potassium,  thallium,  cadmium,  bismuth,  lead,  alumi- 

*  J.  J.  Thomson,  Phil.  Mag.  v.  29,  pp.  358,  441,  1890. 


108]  IONISAT10N    BY   INCANDESCENT   SOLIDS.  189 

nium,  magnesium,  tin,  zinc,  silver  and  mercury ;  sodium  and 
potassium  had  the  highest  conductivity  ;  while  the  conductivity 
of  the  vapours  of  mercury,  tin,  thallium,  did  not  seem  any  greater 
than  that  of  air ;  so  that  the  small  conductivity  actually  observed 
might  have  been  due  to  the  presence  of  air  and  not  to  the  vapour 
of  the  metal. 


Application  of  the  leak  through  hot  gases  to  determine  the 
amount  of  work  required  to  ionise  a  gas. 

108.  By  measuring  the  current  through  a  gas  we  can  deter- 
mine the  number  of  ions  in  unit  volume  if  we  know  the  velocity 
of  the  ions  under  a  given  electric  field  :  for  if  R^  and  R2  are  the 
velocities  under  unit  electric  force  of  the  positive  and  negative 
ions  respectively,  n  the  number  of  ions  (of  either  sign)  per  cubic 
centimetre,  L  the  current  under  the  electric  force  X,  then 


If  these  ions  come  from  the  gas  we  may  regard  the  molecules 
of  the  gas  as  dissociating  into  positive  and  negative  ions  and  these 
recombining  to  form  neutral  molecules  ;  the  problem  of  finding 
the  proportion  between  the  number  of  ions  and  the  number  of 
neutral  molecules  is  the  same  as  that  of  finding  the  proportion 
between  the  atoms  and  molecules  in  a  gas  which  is  dissociating. 
This  problem  has  been  solved  and  an  expression  found  for  the  way 
in  which  the  number  of  free  atoms  depends  upon  the  temperature 
(see  Willard  Gibbs,  Equilibrium  of  Heterogeneous  Substances, 
p.  239;  Boltzmann,  Wied.  Ann.  xxn.  p.  39;  J.  J.  Thomson, 
Applications  of  Dynamics  to  Physics  and  Chemistry,  p.  193). 
When  the  number  of  free  ions  is  small  compared  with  the  num- 
ber of  neutral  molecules  —  as  it  is  in  the  case  of  the  ionisation  of  a 
gas  by  heat,  then  if  n  is  the  number  of  ions  per  unit  volume 


where  p  is  the  pressure  of  the  neutral  molecules,  6  the  absolute 
temperature,  w  the  work  required  to  ionise  one  gramme  of  the 
molecules  of  the  gas,  R  is  the  constant  which  occurs  in  the  equa- 
tion p  =  RpO  for  the  neutral  gas,  p  being  the  density  of  the  gas, 
<£  (0)  is  a  function  of  0  which  does  not  change  rapidly  with  the 
temperature,  so  that  when  the  number  of  ions  changes  very  rapidly 


190  IONISATION    BY   INCANDESCENT    SOLIDS.  [109 

with  the  temperature  as  it  does  in  the  case  of  conduction  through 

_  — 
hot  gases  the  variation  in  n  is  chiefly  due  to  the  factor  e~Ro. 

Hence  if  n1}  nz  are  the  numbers  of  free  ions  at  the  temperatures 
6l  and  02  respectively,  we  have  approximately,  regarding  <£  (6)  and 
w  as  constant, 

nS      w  (  1       1 


hence  if  we  determine  wa/Wi  by  measuring  the  current  through 
the  hot  gas  we  can  find  w.  By  this  method  H.  A.  Wilson*  found 
that  for  air  it  required  about  2100  calories  to  ionise  one  gramme 
of  air.  As  the  ionisation  of  a  gas  consists  in  the  separation  of 
positive  and  negative  charges  it  is  natural  to  express  the  work 
required  to  effect  this  process  as  due  to  the  movement  of  the 
charge  on  the  ion  through  a  certain  difference  of  potential.  If  V 
is  this  potential  difference,  e  the  charge  on  an  ion,  n  the  number 
of  molecules  in  a  gramme  of  air,  in  the  mass  of  a  molecule,  we  have 

neV  =  2100  calories  =  2100  x  4'2  x  107  ergs  ;  nm  =  1 ; 

hence  -  F=  2'1  x  4*2  x  1010; 

m 

for  hydrogen  ej M  —  104  if  M  is  the  mass  of  an  atom  of  hydrogen ; 
hence  if  the  charge  on  the  ion  is  the  same  as  that  on  hydrogen  we 
have  for  air  elm  =  104/28,  hence 

F=2'5  x  108  =  2-o  volts. 

Thus  the  work  done  in  ionising  a  molecule  of  air  corresponds 
to  moving  the  charges  through  about  2 '5  volts. 

The  distribution  of  potential  near  Glowing  Electrodes. 

109.  We  shall  confine  ourselves  to  the  case  when  the  current 
is  passing  between  two  parallel  plane  electrodes.  If  one  of  these 
be  hot  and  the  other  cold — too  cold  to  produce  any  ionisation 
at  its  surface — the  current  will  be  carried  entirely  by  ions  of 
one  sign,  the  electric  force  will  therefore  increase  continuously 
from  the  hot  plate  to  the  cold  one,  and  (see  Art.  101)  the  dis- 
tribution of  potential  will  be  represented  by  a  curve  similar  to 
that  in  Fig.  48,  the  lower  electrode  being  the  hotter  of  the  two. 
Similar  curves  will  represent  the  distribution  of  potential  when 
*  H.  A.  Wilson,  Phil.  Trans.  A.  197,  p.  415,  1901. 


109] 


IONISATION   BY   INCANDESCENT   SOLIDS. 


191 


both  plates  are  hot  provided  the  temperature  of  the  negative  plate 
is  not  high  enough  for  negative  as  well  as  positive  ions  to  be  pro- 
duced at  the  plate,  for  it  is  evident  that  in  this  case  the  current 
has  to  be  carried  entirely  by  positive  ions.  When  however  both 


2468  cms. 
Fig.  48. 

plates  are  hot  enough  to  ionise  the  gas  and  the  negative  so  hot 
that  negative  as  well  as  positive  ions  are  produced,  then  when  the 
field  is  so  strong  that  most  of  the  positive  ions  are  driven  from  the 
positive  plate  and  the  negative  ions  from  the  negative  plate,  we 
shall  have  an  excess  of  positive  ions  at  the  negative  plate,  so  that 
in  the  region  the  potential  curve  will  be  concave,  and  of  negative 
ions  at  the  positive,  which  will  make  the  potential  curve  convex, 
and  the  potential  curve  will  be  like  the  higher  curve  in  Fig.  49, 


3  cms. 


the  straight  part  in  the  middle  showing  that  except  close  to  the 
plates  there   are   approximately  equal  numbers  of  positive  and 
negative  ions  present.    Curves  similar  to  these  for  the  distribution 
of  potential  have  been  obtained  by  H.  A.  Wilson*  and  Marxf. 
When  the  hot  plates  are  made  of  different  materials  Pettinelli 

*  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 
f  Marx,  Drude's  Ann.  ii.  p.  768,  1900. 


192  IONISATION   BY   INCANDESCENT  SOLIDS.  [109 

and  Marolli*  have  shown  that  the  magnitude  of  the  current 
depends  upon  which  metal  is  used  as  the  cathode,  thus  with 
electrodes  of  carbon  and  iron  the  current  when  the  carbon  was 
cathode  was  three  or  four  times  greater  than  when  the  iron 
was  cathode :  they  state  that  the  current  is  greatest  where  the 
more  porous  substance  is  used  as  the  cathode.  These  effects  are 
much  more  marked  at  high  than  at  low  temperatures;  it  is  pro- 
bable that  they  clo  not  commence  until  the  temperature  is  high 
enough  to  produce  negative  ions. 

The  difference  in  the  velocities  of  the  ions  produces  very 
marked  unipolar  effects  in  the  current,  i.e.  the  current  with  the 
same  electromotive  force  is  very  much  greater  in  one  direction 
than  the  opposite ;  we  can  very  easily  see  the  reason  for  this,  for 
take  the  case  where  only  one  electrode  is  hot  enough  to  ionise 
the  gas,  then  jwe  see  from  equation  (1),  p.  195  that  the  current 
is  proportional!  to  the  velocity  under  unit  force  of  the  ion  carrying 
the  current.  As  the  velocity  of  the  negative  ion  is  greater  than 
that  of  the  positive,  the  current  will  be  greater  when  it  is  carried 
by  the  negative  ions  than  when  it  is  carried  by  the  positive.  It 
must  be  remembered  that  the  ratio  of  the  velocities  of  the  ions 
produced  by  an  incandescent  metal  depends  very  largely  upon  the 
temperature.  Thus  McClellandf  who  measured  it  in  air  at  the 
ordinary  temperature  (the  ions  having  been  blown  from  the  in- 
candescent wire  to  the  place  of  observation),  found  that  the 
velocity  of  the  negative  ions  was  only  about  25  per  cent,  greater 
than  that  of  the  positive,  while  H.  A.  WilsonJ  who  measured  this 
ratio  at  high  temperatures  for  the  ions  produced  when  salts 
were  volatilised  in  flames  or  hot  air,  found  that  at  1000°  C. 
the  velocity  of  the  negative  ion  was  for  the  salts  of  the  alkali 
metals  3*6  and  for  those  of  the  alkali  earths  7  times  that  of  the  posi- 
tive. At  2000°  C.  the  velocity  of  the  negative  ions  was  for  the  alkali 
metals  seventeen  times  that  of  the  positive.  The  absolute  values 
were  still  more  different,  thus  McClelland  found  for  the  velocity 
under  a  potential  gradient  of  a  volt  per  cm.  velocities  ranging  from 
•006  cm./sec.  to  '03  cm./sec.,  while  Wilson  at  1000°  C.  found 
26  cm./sec.  for  the  negative,  and  7*2  cm./sec.  for  the  positive ;  at 
2000°  C.  the  values  were  respectively  1030  cm./sec.  and  62  cm./sec. 

*  Pettinelli  and  Marolli,  Atti  delta  Accad.  del  Lincei,  v.  p.  136,  1896. 
t  M'Clelland,  Proc.  Camb.  Phil  Soc.  x.  p.  241,  1899. 
$  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 


CHAPTER  IX. 

IONISATION   IN  GASES  FROM  FLAMES. 

110.  IT  has  been  known  for  more  than  a  century  that  gases 
from  flames  are  conductors  of  electricity  :  a  well-known  applica- 
tion of  this  fact — the  discharge  of  electricity  from  the  surface  of 
a  non-conductor  by  passing  a  flame  over  it — was  used  by  Volta  in 
his  experiments  on  Contact  Electricity.  We  shall  not  attempt 
to  give  any  historical  account  of  the  earlier  experiments  on  this 
subject,  because  the  conditions  in  these  experiments  were  generally 
such  that  the  interpretation  of  the  results  obtained  is  always  ex- 
ceedingly difficult  and  often  ambiguous :  the  reason  of  this  is 
very  obvious — to  investigate  the  electrical  conditions  of  the  flame 
wires  are  generally  introduced,  these  become  incandescent  and  so 
at  once  add  to  the  electrical  phenomena  in  the  flame  the  very 
complicated  effects  we  have  been  discussing  in  the  last  chapter. 

The  gases  which  come  from  the  flame,  even  when  they  have 
got  some  distance  away  from  it  and  have  been  cooled  by  the 
surrounding  air,  possess  for  some  time  considerable  conductivity, 
and  will  discharge  an  insulated  conductor  placed  within  their 
reach.  The  conductivity  can  be  entirely  taken  out  of  the  gas  by 
making  it  pass  through  a  strong  electric  field,  this  field  abstracts 
the  ions  from  the  gas,  driving  them  against  the  electrodes  so  that 
when  the  gas  emerges  from  the  field,  although  its  chemical  com- 
position is  unaltered  its  conducting  power  is  gone.  This  result 
shows  too  that  no  uncharged  radio-active  substances,  such  as 
emanate  from  thorium  and  some  other  substances,  are  produced 
in  the  flame,  these  would  not  be  taken  out  by  the  field  so  that  if 
they  existed  the  conductivity  of  the  gas  would  not  be  destroyed 
by  the  field.  If  not  driven  out  of  the  gas  by  an  electric  field  the 
ions  are  fairly  long  lived.  Thus  in  some  experiments  Giese 

T.  G.  13 


194  IONISATION   IN  GASES  FROM   FLAMES.  [110 

noticed  that  the  gas  retained  appreciable  conductivity  6  or  7 
minutes  after  it  had  left  the  flame.  The  ions  stick  to  any  dust 
there  may  be  in  the  air  and  then  move  very  slowly  so  that  their 
rate  of  recombination  becomes  exceedingly  slow.  McClelland*  has 
shown  that  the  velocity  of  the  ions  under  a  given  electric  force 
decreases  very  much  as  they  recede  from  the  flame ;  thus  close  to 
the  flame  the  velocity  under  the  force  of  a  volt  per  centimetre 
was  "23  cm. /sec.,  while  some  distance  away  from  it  the  velocity 
was  only  '04  cm./sec. 

In  order  that  a  conductor  should  be  discharged  by  a  flame  it 
is  not  necessary  that  it  should  be  placed  where  the  gases  from 
the  flame  would  naturally  strike  it — thus  for  example  it  will  be 
discharged  if  placed  underneath  a  Bunsen  flame.  The  explanation 
of  this  is  that  the  electric  field  due  to  the  charged  conductor 
drags  out  of  the  flame  and  up  to  the  conductor  ions  of  opposite 
sign  to  the  charge. 

This  ionised  gas  is  produced  by  flames  of  coal  gas  whether 
luminous  or  not,  by  the  oxy-hydrogen  flame,  by  the  alcohol  flame 
of  a  spirit  lamp,  by  a  flame  of  carbonic  oxide ;  it  is  not  however 
produced  in  very  low  temperature  flames  such  as  the  pale  lambent 
flame  of  ether.  Thus  to  produce  the  ionised  gas  high  temperature 
as  well  as  chemical  combination  is  required.  That  chemical  com- 
bination alone  is  insufficient  to  produce  ionisation  is  shown  by  the 
case  of  hydrogen  and  chlorine  which  do  not  conduct  even  when 
combining  under  ultra-violet  light f.  BraunJ  has  shown  that 
in  the  explosive  wave  produced  in  the  combination  of  certain 
gases  there  is  ionisation,  but  in  this  case  there  is  also  very  high 
temperature. 

In  the  coal  gas  flame  the  part  where  the  gas  comes  in  contact 
with  the  air  and  where  there  is  most  combustion  is  positively 
electrified,  while  the  interior  of  the  flame  is  negatively  elec- 
trified, this  accounts  for  the  effect  produced  by  holding  a 
negatively  electrified  body  near  the  flame,  the  luminous  part 
turns  to  the  negative  body,  and  if  this  is  near  stretches  out  until 
it  comes  into  contact  with  it ;  if  the  flame  be  placed  between  two 

*  McClelland,  Phil.  Mag.  v.  46,  p.  29,  1898. 

f  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  xi.  p.  90,  1901. 

J  Braun,  Zeitschrift  fur  Physikalische  Chemie,  xiii.  p.  155,  1894. 


110] 


IONISATION  IN  GASES   FROM   FLAMES. 


195 


oppositely  charged  plates  the  bright  outer  portion  of  the  flame 
is  attracted  towards  the  negative  plate  while  the  inner  portion 
moves,  but  less  markedly,  towards  the  positive  plate.  This  effect 
is  illustrated  by  Fig.  50  taken  from  a  paper  by  Neureneuf*;  in 


Fig.  50. 

some  experiments  made  by  Holtz  f,  one  of  which  is  figured  in 
Fig.  51,  the  flame  was  divided  by  the  electric  field  between  the 


Fig.  51. 

plates  into  two  sheets ;  the  reader  will  find  many  other  interesting 
experiments  on  the  effect  of  an  electric  field  on  the  shape  of 
flames  in  the  papers  by  Neureneuf  and  Holtz.  It  appears  from 
these  results  that  in  the  bright  portion  of  the  flame  where  combus- 
tion is  taking  place  there  is  an  excess  of  positive  electricity,  while 
in  the  unburnt  coal  gas  there  is  an  excess  of  negative,  a  fact 
discovered  a  long  time  ago  by  PouilletJ.  If  the  hydrogen  and 
oxygen  were  ionised  by  the  heat,  then  since  negative  ions  of 
oxygen  combine  with  positive  ions  of  hydrogen  to  form  water,  the 

*  Neureneuf,  Annales  de  Chim.  et  de  Phys.  v.  2,  p.  473,  1874. 

t  Holtz,  Carl  Repert.  xvii.  p.  269,  1881. 

t  Pouillet,  Ann.  de  Chim.  et  de  Phys.  xxxv.  p.  410,  1827. 

13—2 


196  IONISATION  IN  GASES    FROM   FLAMES.  [110 

negative  oxygen  ions  and  the  positive  hydrogen  ones  would  get 
used  up,  and  there  would  be  an  excess  of  positive  electricity  in 
the  oxygen  and  of  negative  in  the  hydrogen.  It  is  possible  too 
that  at  a  temperature  corresponding  to  that  of  vivid  incandescence 
in  a  solid  the  molecules  of  a  gas  may  like  those  of  a  solid  give  out 
the  negative  corpuscles,  on  this  account  there  would  be  a  tendency 
for  the  hotter  parts  of  the  flame  to  be  positively  the  colder 
negatively  electrified.  When  as  in  luminous  flames  we  have 
small  particles  of  solid  carbon  raised  to  the  temperature  of  vivid 
incandescence  the  electrical  effects  are  complicated  by  those  due 
to  incandescent  solids  which  as  we  have  seen  in  the  last  chapter 
are  very  considerable. 

When  two  wires  connected  together  through  a  sensitive 
galvanometer  are  placed  in  different  parts  of  the  flame  currents 
flow  through  the  galvanometer;  suppose  one  of  the  wires  is 
placed  in  the  cool  inner  portion  of  the  flame  where  there  is  an 
excess  of  negative  electricity,  while  the  other  wire  is  placed  at 
the  outside  of  the  flame  where  there  is  an  excess  of  positive 
electricity  there  will,  neglecting  any  ionisation  due  to  the  wire, 
be  a  current  from  the  hot  outer  portion  of  the  flame  to  the  cool 
inner  portion  through  the  galvanometer :  the  wire  in  the  outer 
portion  will  however  certainly  be  raised  to  incandescence  if  its 
temperature  keeps  so  low  that  only  positive  Jons  are  produced  at 
its  surface,  then  there  will  on  this  account  be  a  current  of 
electricity  from  the  hot  to  the  cool  part  of  the  flame  through  the 
flame  and  thus  in  the  opposite  direction  to  the  previous  current. 
If  however  the  wire  got  so  hot  that  it  emitted  more  negative 
than  positive  ions  the  effect  of  the  incandescence  of  the  wires 
would  be  to  increase  instead  of  diminishing  the  current  due  to  the 
flame  itself.  Thus  we  see  that  these  currents  will  vary  in  a 
complex  way  with  the  temperature.  For  an  account  of  the 
currents  which  can  thus  be  tapped  from  a  flame  and  for  other 
electrical  properties  of  flames  we  must  refer  the  reader  to  the 
papers  of  Erman*,  Hankelf,  Hittorf J,  Braun§,  Herwig||,  and 

*  Erman,  Gilbert.  Ann.  xi.  p.  150,  1802 ;  xxii.  p.  14,  1806. 

t  Hankel,  Pogg.  Ann.  Ixxxi.  p.  213,  1850 ;  cviii.  p.  146,  1859. 

J  Hittorf,  Pogg.  Ann.  cxxxvi.  p.  197,  1869 ;  Jubelbd.  p.  430,  1874. 

§  Braun,  Pogg.  Ann.  cliv.  p.  481,  1875. 

||  Herwig,  Wied.  Ann.  i.  p.  516,  1877. 


Ill]  IONISATION   IN   GASES   FROM   FLAMES.  197 

especially  of  Giese*,  who  was  the  first  to  suggest  that  the 
conduction  of  electricity  through  flames  and  hot  gases  was  due 
to  the  motion  of  charged  ions  distributed  through  the  gases : 
there  is  a  very  complete  account  of  these  researches  in  Wiede- 
mann's  Elektricitdt,  bd.  IV.  B,  chap.  4. 

Conductivity  of  Gases  containing  Salt   Vapours. 

111.  When  the  vapours  of  salts  are  introduced  into  a  flame 
the  conductivity  between  metallic  terminals  is  very  greatly  in- 
creased, and  the  electrical  properties  are  simpler  and  more  regular 
than  in  pure  flames ;  the  laws  of  the  flow  of  electricity  through 
these  salt-laden  flames  have  been  investigated  by  Arrheniusf 
and  H.  A.  Wilson J.  The  method — devised  by  Arrhenius  and 
adopted  by  Wilson — of  introducing  the  salt  into  the  flame  was 
as  follows  :  a  dilute  solution  of  the  salt  was  sprayed  into  ex- 
ceedingly fine  drops  by  a  Gouy  sprayer,  the  spray  got  well  mixed 
with  the  coal  gas  on  its  way  to  the  burner,  and  in  the  flame  the 
water  evaporated  and  the  salt  vaporised.  The  amount  of  salt 
supplied  to  the  flame  in  unit  time  was  estimated  by  determining 
the  rate  at  which  a  bead  of  salt  introduced  into  an  equal  and 
similar  flame  so  as  to  produce  the  same  coloration  as  that  pro- 
duced by  the  spray  in  the  original  flame  burnt  away.  The  salts 
used  were  chiefly  the  haloid  and  oxy-salts  of  the  alkali  metals 
and  earths.  The  conductivity  due  to  the  salt  was  determined  by 
subtracting  from  the  current  observed  when  the  salt  was  in  the 
flame  the  current  with  the  same  electromotive  force  in  the  pure 
flame.  It  was  found  that  when  the  concentration  of  the  solutions 
is  small,  equivalent  solutions  §  of  all  salts  of  the  same  metal 
impart  the  same  conductivity  to  the  flame.  With  large  concen- 
tration this  is  no  longer  the  case,  the  oxy-salts  giving  greater 
conductivity  than  the  haloid  salts.  According  to  Arrhenius  aU 
the  salts  in  the  flame  are  converted  into  hydroxides,  so  that  what- 
ever salts  are  used,  the  metal  in  the  flame  always  occurs  in  the 
same  salts.  The  relation  between  the  current  and  the  electro- 

*  Giese,  Wied.  Ann.  xvii.  pp.  1,  236,  519,  1882 ;  xxxviii.  p.  403,  1889. 
f  Arrhenius,  Wied.  Ann.  xlii.  p.  18,  1891. 
£  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 

§  Equivalent  solutions  are  those  in  which  the  weight  of  salt  per  litre  is  pro- 
portional to  the  molecular  weight  of  the  salt. 


198 


IONISATION   IN  GASES   FROM   FLAMES. 


[in 


motive  force  is  represented  by  Fig.  5 2 taken  from  Wilson's  paper: 
we  see  that  the  curves  resemble  in  many  respects  those  given  in 


20        40        60        80        100      120      14O      160      ISO     200  CeJ  S. 

(200  cells  =  360  volts) 
Fig.  52. 

Fig.  4,  which  represent  this  relation  for  the  typical  ionised  gas. 
There  is  one  well  marked  difference,  however,  in  the  typical  curve, 
the  straight  part  is  horizontal,  i.e.  the  current  does  not  increase 
at  all  with  the  electromotive  force ;  in  the  case  of  the  salt  vapour 
the  straight  part  is  inclined  at  a  finite  angle  to  the  horizontal, 
indicating  a  slow  but  steady  increase  of  the  current  with  the 
electromotive  force.  The  cause  of  this  difference  between  the 
normal  curves  and  the  curve  for  the  flame  is  I  think  that  in  the 
latter  case  the  ionisation  takes  place  mainly  at  the  surface  of  the 
electrodes  (for  the  proof  of  this  see  p.  172).  We  have  thus  two 
sources  of  supply  for  the  ions,  so  that  to  '  saturate '  the  current 
we  must  use  up  all  the  ions  from  both  sources,  i.e.  all  the  negative 
ions  produced  at  the  negative  electrode,  and  all  the  positive  ions 
at  the  positive  electrode  must  be  sent  into  the  gas  and  used  to 
carry  the  current.  Now  as  we  shall  see  the  velocity  of  the 
negative  ions  in  flames  containing  salt  vapours  is  very  much 
greater  than  that  of  the  positive,  so  that  the  negative  ions  will 
be  much  more  easily  detached  from  the  negative  electrode  than 
the  slowly  moving  positive  ions  from  the  positive  electrode :  thus 
we  shall  exhaust  the  supply  of  the  negative  ions  long  before  we 
do  that  of  the  positive.  If  all  the  current  were  carried  by  the 
negative  ions  it  would  be  saturated  as  soon  as  the  supply  of  these 
was  exhausted ;  in  practice  a  small  but  appreciable  fraction  of  the 
current  is.  carried  by  the  positive  ions,  so  that  after  the  supply  of 
negative  ions  is  exhausted  the  current  will  go  on  slowly  increasing 
for  a  long  range  of-  potential  difference  until  finally,  the  supply  of 

''Y?^-'- 


112] 


IONISATION   IN   GASES   FROM   FLAMES. 


199 


positive  ions  is  exhausted,  and  then  and  not  till  then  the  current 
will  become  independent  of  the  potential  difference  between  the 
electrodes.  The  difference  between  the  field  required  to  drive  all 
the  ions  from  the  negative  and  positive  electrodes  is  well  illus- 
trated by  an  experiment  of  Wilson's,  in  which  only  one  of  the 
electrodes  was  hot,  the  other  was  too  cold  to  give  rise  to  any 
ionisation ;  in  this  case  when  the  hot  electrode  was  negative  the 
current  was  saturated  with  a  comparatively  small  potential  differ- 
ence, while  it  required  an  exceedingly  large  potential  difference 
to  saturate  the  current  when  the  hot  electrode  was  positive. 

Another  proof  in  addition  to  those  given  on  p.  172  that  the 
ionisation  at  the  electrodes  is  greater  than  in  the  body  of  the  gas 
is  afforded  by  experiments  made  with  the  electrodes  at  different 
distances  apart.  If  the  greater  part  of  the  ionisation  took  place 
in  the  body  of  the  gas  the  saturation  current  would  be  proportional 
to  the  distance  between  the  electrodes.  In  the  case  of  conduction 
through  flames  containing  vapours  of  salts  Wilson  has  shown  that 
the  saturation  current  is  very  approximately  independent  of  the 
distance  between  the  electrodes. 

112.  The  conductivity  given  to  the  flame  by  the  salts  of  the 
different  alkali  metals  under  the  same  condition  as  to  temperature, 
potential  difference  and  concentration.  The  Caesium  salts  conduct 
the  best,  and  then  follow  in  order  the  salts  of  Rubidium, 
Potassium,  Sodium,  Lithium,  and  Hydrogen.  The  order  of  the 
conductivities  is  thus  the  same  as  that  of  the  atomic  weights  of 
the  metals,  and  the  difference  between  the  metals  is  very  large, 
as  is  shown  by  the  following  table  given  by  H.  A.  Wilson : 


Chlorides. 

Nitrates. 

Potential  Difference 

5-60 

•795 

•237 

5-60 

•795 

•237 

Current 

Current 

Caesium 

123 

60-5 

22-2 

303 

115 

36-6 

Rubidium 

41-4 

26-4 

11-3 

213 

82-4 

25-9 

Potassium 

21-0 

13-4 

5-75 

68-4 

29-3 

9-35 

Sodium 

3-49 

2-45 

1-15 

3-88 

2-67 

1-32 

Lithium 

1-29 

•87 

•41 

1-47 

•99 

•53 

Hydrogen 

•75 

... 

•27 

» 

200  IONISATION   IN  GASES    FROM  FLAMES.  [113 

On  the  Variation  of  Conductivity  with  the  strength  of  the 

Solution. 

113.  Arrhenius  came  to  the  conclusion  that,  using  the  same 
salt,  the  conductivity  was  proportional  to  the  square  root  of  the 
concentration,  while  H.  A.  Wilson  considered  that  the  application 
of  this  simple  law  was  restricted  in  the  case  of  the  oxy-salts  to 
extremely  dilute  solutions,  and  that  although  the  range  of  its 
application  was  more  extended  in  the.  case  of  the  haloid  salts,  the 
agreement  was  only  approximate.  If  we  refer  to  the  general 
theory  of  conduction  through  an  ionised  gas  (see  page  68)  we  find 
that  the  conductivity  when  the  current  is  far  from  saturation  is 
proportional  to  ql,  where  q  is  the  number  of  ions  produced  per 
second  in  a  cubic  centimetre  of  the  gas.  In  the  case  of  the  salt 
vapour  q  will  be  proportional  to  the  number  of  molecules  of  salt 
in  a  cubic  centimetre  of  the  gas,  and  will  thus  be  proportional  to 
the  strength  of  the  solution.  This  result  is  derived  from  the 
study  of  the  case  when  ioriisation  takes  place  throughout  the 
volume  of  the  gas;  it  will  however  be  applicable  in  its  main 
features  to  the  case  when  the  ionisation  only  takes  place  near  the 
surface  of  the  electrodes,  provided  the  thickness  of  the  layers  in 
which  the  ionisation  occurs  is  large  compared  with  the  average 
distance  between  the  molecules  of  the  salt,  and  that  the  dis- 
tribution of  potential  between  the  electrodes  is  not  affected  by 
the  concentration  of  the  salt ;  this  second  supposition  is  probably 
not  true.  The  above  reasoning  only  applies  to  the  case  when  the 
current  is  far  from  the  saturation  value ;  when  it  approaches  this 
value  the  current  is  proportional  to  q  and  not  to  q12 ;  thus  we 
should  expect  that  in  the  case  of  currents  through  flames  under 
large  electromotive  forces  Arrhenius'  law  would  cease  to  be  true, 
and  the  current  would  be  proportional  to  the  concentration.  In- 
spection of  the  curves  given  in  Fig.  53  taken  from  a  paper  by 
Smithells,  Dawson  and  Wilson*  will  show  that  the  variations  of 
the  current  with  the  strength  of  the  solution,  even  when  the 
current  is  well  past  the  knee  of  the  curve  representing  the  relation 
between  current  and  potential  difference,  are  much  less  than  they 
would  be  if  they  varied  directly  as  the  concentration;  in  fact, 
even  in  this  stage  they  are  much  more  nearly  proportional  to  the 
square  root  than  to  the  first  power  of  the  concentration.  This 
*  Smithells,  Dawson  and  Wilson,  Phil.  Trans.  A.  193,  p.  89,  1900. 


113] 


IONISATION    IN    GASES    FROM    FLAMES. 


201 


effect  is  rather  difficult  to  account  for.  May  it  be  due  to  the 
thickness  of  the  layer  through  which  the  ionisation  extends  de- 
pending to  some  extent  on  the  concentration  ?  This  would  be 


Fig.  53. 

the  case  if  the  ionisation  were  produced  by  radiation  or  corpuscles 
proceeding  from  the  electrodes,  the  absorption  of  the  radiation 
being  due  in  whole  or  in  part  to  the  work  done  in  ionising  the 
salt ;  for  consider  the  extreme  case  where  the  absorption  is  wholly 
due  to  the  ionisation  of  the  salt,  then  if  the  absorption  were  great 
enough  to  stop  the  radiation  from  one  electrode  before  it  reached 
the  other,  the  amount  of  ionisation,  and  therefore  the  saturation 
current,  would  be  independent  of  the  concentration  ;  with  large 
concentrations  the  ionisation  would  be  confined  to  a  thin  layer 
near  the  electrodes,  with  small  concentrations  this  layer  would  be 
thicker,  but  the  total  amount  of  ionisation  would  be  the  same 
in  the  two  cases.  If  the  radiation  was  not  completely  absorbed 
in  the  space  between  the  electrodes  the  amount  of  ionisation 
would  increase  with  the  concentration,  but  its  rate  of  increase 
would  be  slower  than  that  of  the  concentration.  Wilson  has 
shown  (see  p.  210)  that  at  very  high  temperatures  the  saturation 
current  is  proportional  to  the  concentration. 


202 


IONISATION   IN   GASES    FROM   FLAMES. 


[114 


Velocity  of  the  Ions. 

114.  The  velocity  of  the  ions  in  flames  containing  salt  vapours 
has  been  determined  by  H.  A.  Wilson*,  who  used  a  method  of 
which  the  principle  is  as  follows.  Suppose  that  in  a  flame  we 
have  two  electrodes  one  vertically  over  the  other,  and  that  we 
introduce  a  bead  of  salt  just  underneath  the  upper  electrode,  the 
vapour  from  this  bead  will  be  carried  along  by  the  upward  rush 
of  gases  in  the  flame,  and  unless  the  ions  in  the  salt  vapour  are 
driven  downwards  by  the  electric  field  between  the  electrodes, 
none  of  them  will  reach  the  lower  electrode.  If  however  the  ions 
from  the  salt  do  not  reach  the  electrode  the  current  between  the 
electrodes  will  be  unaffected  by  the  presence  of  the  salt.  Thus 
when  the  potential  difference  between  the  electrodes  is  small  the 
current  will  not  be  increased  by  the  introduction  of  the  salt,  but 
as  soon  as  the  electric  force  between  the  electrodes  is  sufficient  to 
drive  one  of  the  ions  against  the  blast  in  the  flame,  the  current 
will  be  increased  by  the  bead  of  salt;  This  is  illustrated  by  the 
curve  in  Fig.  54  taken  from  Wilson's  paper ;  we  see  that  when 


50, 


80 


160  240 

Fig.  54. 


300 


400        volts 


the  upper  electrode  was  positive  the  current  was  not  increased  by 
the  bead  until  the  potential  difference  between  the  electrodes  was 
about  100  volts,  while  for  greater  differences  of  potential  the  bead 
produced  a  substantial  increase  in  the  current.  Thus  when  there 
was  a  difference  of  100  volts  between  the  electrodes,  the  smallest 
electric  force  in  the  space  traversed  by  the  ion  must  be  just 

*  H.  A.  Wilson,  Phil.  Trans.  A.  192,  p.  499,  1899. 


114]  IONISATION   IN   GASES   FROM   FLAMES.  203 

sufficient  to  give  to  the  positive  ion  a  downward  velocity  equal 
to  the  upward  velocity  of  the  gas  in  the  flame.  Since  the 
electric  field  is  not  uniform  between  the  electrodes  (see  p.  191),  it 
is  necessary  to  measure  the  distribution  of  potential  between  the 
electrodes  in  order  to  determine  the  minimum  electric  force ; 
when  this  and  the  upward  velocity  of  the  gas  in  the  flame  are 
known  we  can  determine  the  velocity  of  the  ions  in  a  flame 
under  a  given  electric  force.  By  this  and  similar  methods  Wilson 
deduced  the  following  values  for  the  velocities  of  the  ions  under 
an  electric  force  of  a  volt  per  centimetre. 

In  a  flame  whose  temperature  was  estimated  to  be  about 
2000°  C.,  the  velocity  of  the  negative  ion,  whatever  salts  were  put 
in  the  flame,  was  about  1000  cm./sec. 

The  velocities  of  the  positive  ions  of  salts  of  Caesium,  Rubidium, 
Potassium,  Sodium,  and  Lithium  were  all  equal,  and  were  about 
62  cm./sec. 

In  a  stream  of  hot  air  whose  temperature  was  estimated  at 
1000°C.  the  following  results  were  obtained  for  the  velocities 
under  a  potential  gradient  of  1  volt  per  cm. 

Negative  ions    ...          ...          ...          ...          ...     26  cm./sec. 

Positive  ions  of  salts  of  Li,  Na,  K,  Rb,  and  Cs     7*2  cm./sec. 
Positive  ions  of  salts  of  Ba,  Sr,  and  Ca          ...     3'8  cm./sec. 

The  absolute  numbers  must  be  regarded  as  only  approximately 
true,  the  relative  values  are  probably  much  more  accurate. 

The  velocities  are  very  much  less  at  1000°  C.  than  they  are 
at  2000°  C.,  but  we  notice  that  while  the  negative  ion  at  the 
lower  temperature  moves  at  only  1/40  of  its  pace  at  the  higher,  the 
velocity  of  the  positive  ion  is  by  the  same  fall  in  temperature  only 
reduced  to  about  1/8*5  of  its  value. 

These  determinations  of  the  velocity  throw  some  light  on  the 
character  of  the  ions ;  for  suppose  e  is  the  charge  of  electricity  on 
the  ion,  X  the  electric  force  acting  upon  it,  the  mechanical  force 
acting  on  the  ion  is  equal  to  Xe ;  if  X  is  the  mean  free  path  of 
the  ion,  v  its  velocity  of  translation,  then  the  time  between 
two  collisions  is  \/vt  and  in  this  time  the  force  acting  upon 
it  will  give  it  a  velocity  in  the  direction  of  the  force  equal  to 
Xekjvm,  where  m  is  the  mass  of  the  ion;  the  average  velocity 


204  IONISATION   IN   GASES    FROM   FLAMES.  [114 


parallel  to  X  due  to  the  electric  force  will  therefore  be 
and  this  will  be  the  velocity  with  which  the  ion  will,  under  the 
electric  force,  move  through  the  gas.  >  The  equal  velocity  of  all 
negative  ions  from  whatever  source  they  may  be  derived  might 
at  first  sight  seem  to  indicate  that  as  Arrhenius  supposed  all  the 
salts  were  converted  to  hydroxides  in  the  flame,  and  that  the 
negative  ion  was  in  every  case  the  radicle  OH  :  let  us  calculate 
what  on  this  supposition  would  be  the  velocity  of  the  negative 
ion  at  a  temperature  of  2000°  G.  We  do  not  know  the  free  path 
of  OH  through  a  mixture  of  coal-gas  and  air,  but  as  the  free  path 
of  the  molecule  H2  through  hydrogen  at  0°  C.  and  at  atmospheric 
pressure  is  1*8  x  10~5cm.,  and  the  free  path  ofO2  through  oxygen 
under  the  same  circumstances  is  T06  x  10~5  cm.,  we  may  as  a 
rough  approximation  take  for  the  mean  free  path  of  OH  through 
the  mixture  the  value  1'4  x  10~6  cm.  at  0°C.;  aj  2000°  C.  X  the 
mean  free  path  would  be  this  value  multiplied  by  2273/273,  i.e. 
1'2  x  10~4.  To  get  the  value  of  v  we  remember  that  mv2  is  the 
same  for  all  gases  at  the  same  temperature,  while  at  different 
temperatures  it  is  proportional  to  the  absolute  temperature. 
For  O2  at  0°  C.  v  =  4'25  x  104  cm./sec.,  hence  for  OH  at  0°  C. 
v  =  5-6  x  104  cm./sec.,  and  for  OH  at  2000°  C.  v  =  T6  x  105  :  e/m 
for  OH  is  equal  to  I'l  x  103,  hence  substituting  these  values  in  the 
expression  Xe\/Zvm  and  putting  X  =  108  we  find  for  the  velocity 
under  the  potential  gradient  of  one  volt  per  cm.  37  cm./sec.:  the 
actual  velocity  is  as  we  have  seen  1000  cm./sec.:  hence  we  con- 
clude that  the  radicle  OH  cannot  be  the  carrier  of  the  negative 
charges.  The  great  velocity  of  the  negative  ions  at  these  high 
temperatures  points  to  the  conclusion  that  the  negative  ions 
start  as  corpuscles  and  gradually  get  loaded  by  molecules  con- 
densing round  them  ;  at  temperatures  as  high  as  2000°  the  time 
they  exist  as  free  corpuscles  is  an  appreciable  fraction  of  their  life; 
while  they  are  free  corpuscles  they  have  an  exceedingly  large 
velocity,  so  that  though  this  is  enormously  reduced  when  they 
become  the  nucleus  of  a  cluster,  their  average  velocity  is  very 
considerable.  At  low  temperatures  condensation  takes  place 
much  sooner,  so  that  the  average  velocity  is  lower. 

The  fact  that  under  an  electric  field  the  velocities  of  the 
positive  ions  of  all  the  salts  of  the  univalent  metals  are  the  same, 
shows  that  these  too  become  the  nucleus  of  a  group  whose  size  only 


115]  IONISATION   IN   GASES    FROM   FLAMES.  205 

depends  upon  the  charge  on  the  positive  ion  ;  since  the  velocities 
of  the  positive  ions  for  the  divalent  metals  while  equal  among 
themselves  are  less  than  those  of  the  monovalent  metals,  we  con- 
clude that  these  divalent  ions  become  the  centres  of  clusters  more 
complex  than  those  which  collect  round  the  monovalent  ions. 

Determinations  of  the  velocities  of  the  ions  in  flames  have  also 
been  made  by  Marx*,  he  finds  for  the  velocity  of  the  negative 
ion  the  same  value  as  Wilson,  i.e.  1000  cm./sec.  under  a  potential 
gradient  of  a  volt  per  centimetre,  he  gets  however  for  the  positive 
ions  under  the  same  gradient  considerably  larger  values  than 
Wilson,  i.e.  200  cm./sec.  instead  of  62  cm./sec.  A  calculation 
similar  to  that  just  given  for  the  velocity  of  the  radicle  OH 
shows  that  a  velocity  of  200  cm./sec.  is  of  the  same  order  as  the 
velocity  at  2000°  C.  of  an  atom  of  hydrogen  in  an  electric  field. 

\ 

Transverse  Electromotive  Force  produced  by  a  magnetic  field 
acting  on  a  flame  carrying  a  current. 

115.  If  an  electric  current  is  flowing  through  a  flame  parallel 
to  the  direction  x,  and  a  magnetic  force  at  right  angles  to  this 
direction,  say  parallel  to  the  direction  y,  is  applied  to  the  flame, 
a  transverse  electromotive  force  is  produced  which  is  at  right 
angles  to  both  x  and  y.  This  electromotive  force  has  been  detected 
and  measured  by  Marx~f*.  The  general  explanation  of  this  effect, 
which  is  analogous  to  the  '  Hall '  effect  in  metals,  is  easy ;  the 
calculation  of  its  magnitude  except  in  a  few  special  cases  is  how- 
ever beset  by  difficulties. 

As  there  is  a  current  parallel  to  x  flowing  through  the  flame, 
the  average  direction  of  the  positive  ions  will  be  along,  say,  the 
positive  direction  of  x,  that  of  the  negative  ions  in  the  opposite 
direction.  Let  V  be  the  average  velocity  of  the  positive  ions, 
V  that  of  the  negative,  if  these  are  moving  in  a  magnetic  field 
where  the  magnetic  force  H  is  parallel  to  y,  they  will  be  subject 
to  mechanical  forces  tending  to  move  them  in  the  same  direction, 
this  direction  being  parallel  to  z,  at  right  angles  to  both  x  and  y. 
The  magnitudes  of  the  mechanical  forces  acting  on  the  positive 
and  negative  ions  are  respectively  HeV and  HeV,  where  e  is  the 

*  Marx,  Drude's  Ann.  ii.  p.  768,  1900. 
f  Ibid.  p.  798,  1900. 


206  IONISATION   IN   GASES    FROM   FLAMES.  [115 

charge  on  an  ion.  The  displacement  of  the  ions  under  these 
forces  will  (if  V  is  not  equal  to  V)  produce  a  current  of  electricity 
through  the  flame  parallel  to  z ;  if  however  the  ions  cannot 
escape  in  this  direction  the  current  will  soon  stop,  as  the  accu- 
mulation of  ions  will  produce  a  back  pressure  and  an  electrostatic 
field  which  will  balance  the  effect  of  the  mechanical  forces  arising 
from  the  magnetic  field. 

We  shall  now  proceed  to  deduce  the  equations  which  give  the 
disturbance  produced  by  the  magnetic  field ;  these  equations  are 
not  limited  to  the  case  of  flames,  but  apply  to  all  cases  of  the 
conduction  of  electricity  through  a  gas  containing  ions. 

Let  the  direction  of  the  primary  current,  i.e.  the  current  before 
the  magnetic  field  is  applied,  be  taken  as  the  axis  of  x,  let  the 
magnetic  force  act  downwards  at  right  angles  to  the  plane  of 
the  paper :  then  the  force  on  the  ions  will  be  in  the  plane  of 
the  paper  and  at  right  angles  to  the  axis  of  x ;  we  shall  take  the 
axis  of  z  in  this  direction. 

Let  H  be  the  intensity  of  the  magnetic  force, 

X,  Z  the  components  of  the  electric  force  parallel  to  the 

axes  of  x  and  z  respectively, 
u,  v  the  velocities  of  the  positive  and  negative  ions  under 

unit  electric  force, 
Pit  Pz  the  pressures  at  any  point  due  to  the  positive  and 

negative  ions  respectively, 
ra,  n  the  number  of  positive  and  negative  ions  per  cubic 

centimetre  at  any  point. 

We  shall  assume  that  these  ions  behave  like  a  perfect  gas,  so 
that  P!  =  Rm,  p2  —  Rn,  where  R  is  a  constant  proportional  to  the 
absolute  temperature. 

Let  us  consider  first  the  positive  ions,  their  velocity  parallel 
to  the  axis  of  x  is  Xu,  hence  the  mechanical  force  on  an  ion 
parallel  to  z  due  to  the  magnetic  field  is  euXH,  the  force  on  the 
ion  due  to  the  electric  field  is  Ze,  and  the  force  on  the  ions  in  unit 
volume  due  to  the  variation  in  the  pressure  at  different  points  in 
the  field  is  —  dpi/dz,  hence  the  total  force  parallel  to  z  on  the 
positive  ions  in  unit  volume  is  equal  to 

-<&  + 


115]  IONISATION   IN   GASES   FROM  FLAMES.  207 

and  the  number  crossing  in  unit  time  one  square  centimetre  of 
surface  at  right  angles  to  z  is  equal  to 

U    (       dpl  ,     TTTT         rr^} 

-    -  -f  +  me  (uXH  +  Z)\, 


similarly  the  flux  parallel  to  x  is  equal  to 


or,  if  we  neglect  terms  depending  upon  Hz  the  term  uZH  may 
be  omitted  and  the  flux  parallel  to  x  is  then 

u  (      dpl  v  ) 

-  ]  —  -f-  +  meX    . 
e  {      dx  } 

Similarly  the  flux  of  the  negative  ions  parallel  to  z  is  equal  to 


and  the  flux  parallel  to  x  to 

v  f     dpz  rr 

-     — j-  —  neX 
e  \      dx 

Let  q  be  the  number  of  ions  produced  in  one  cubic  centimetre 
of  the  gas  in  one  second,  anm  the  number  of  ions  which  recombine 
in  one  second  in  unit  volume ;  then  by  the  equation  of  continuity 
we  have  when  things  are  in  a  steady  state, 

u  d  f      dpl  /    VTT      n\  I      u  d   f      dp^  v\ 

-•j-  4  — f-  +  me  (uXH  +  Z)  >  H :- f-  4-  meX  )  =  q  — 

e  dz  {      dz  }       e  dx\      dx  J 

v  d  (      dp%  /  VTT      r7\\      v  d  /     dp2 

— j-  4 ^  4-  ne  (vJLii  —  Z)  >  H ^—     —  7 

e  dz  {      dz  }      e  dx\      ax 

we  have  also,  using  electrostatic  units, 

dX     dZ 

-j-  +  -j-  =  4<7re  (m  —  n), 
dx       dz 

dX     dZ 

and  =-  =  0. 

dz       dx 

Since  p^  =  Rm,  p2  =  Rn,  we  have  as  many  equations  as  there 
are  variables,  plf  p2,  m,  n,  X,  Z.  The  solution  will  however  depend 
very  greatly  upon  the  boundary  conditions;  thus  one  solution 
is  £  =  0,  pl  and  pu  constant,  and  X  independent  of  z  and  the 


208  IONISATION   IN   GASES    FROM   FLAMES.  [115 

same  as  when  the  magnetic  force  is  zero  :  this,  however,  involves  a 
transverse  flux  of  positive  ions  equal  to  mu2XH  and  of  negative 
ions  equal  to  nv2XH,  and  is  not  consistent  with  a  steady  state 
unless  there  is  some  means  for  this  transverse  stream  to  escape. 
If  there  is  no  way  of  escape  for  the  transverse  streams  of  ions 
the  flux  of  the  ions  parallel  to  z  must  vanish  at  the  boundaries  of 
the  gas.  Let  us  suppose  that  it  vanishes  throughout  the  gas,  then 
we  have 

Q  ..................  (1)  ; 

..................  (2). 


Putting  pl  =  Rm,  p2  —  Hn  and  (m  —  n)e  =  p  we  get  from  (1) 
and  (2) 


+  n)     .........  (3); 

6  CLZ 


and  since,  changing  to  electromagnetic  units, 
dp       I   (d*Z     d*Z 

7r-~     + 


where  V  is  the  velocity  of  light  ;  (3)  becomes 

+  n)    ......  (4), 


R      /( 


an  equation  to  find  Z.  In  the  terms  on  the  right-hand  side,  we 
may  put  for  X,  m,  n  the  values  when  H  =  0,  if  we  are  content  to 
neglect  terms  in  H2. 

Since  72  =  9  x  1020,  e  =  I'l  x  1Q-20  (in  electromagnetic  units), 
Ji  =  5  x  10  ~14,  for  a  gas  at  0°  C.,  we  see  that  (4)  may  be  written 

4  x  10~16  (-T-J  +  -r-g  )  =  eXH  (mu  -  nv)  +  Ze(m+  n). 
\  (Lx         (JiiZ   ) 

If  the  sum  of  the  partial  pressures  due  to  the  positive  and 
negative  ions  were  1  atmosphere  e  (m  +  n)  would  be  about  '5,  hence 
we  see  that  if  the  pressure  of  the  ions  is  large  compared  with 
10~15  atmospheres  and  if  Z  does  not  vary  exceedingly  rapidly 
with  x,  a  very  approximate  solution  of  (4)  will  be 

z=XH(nv-mu) 

m  +  n 


115]  IONISATION   IN   GASES   FROM   FLAMES.  209 

This  may  be  written 


e  (m  +  ri)  ' 

where  in  and  ip  are  respectively  the  currents  carried  by  the  negative 
and  positive  ions. 

At  a  place  where  there  is  no  free  electricity  m  —  n\  in  this 
case  (5)  becomes 


This  is  the  formula  usually  employed,  but  we  see  from  the 
preceding  work  it  is  only  applicable  in  a  very  special  case. 

When  solutions  of  KC1  of  various  strengths  were  sprayed  into 
a  flame  Marx*  found  values  of  Z/XH  varying  from  10'18  x  10~€ 
for  the  pure  flame  to  3*7  x  10  ~6  when  a  saturated  solution  of 
KC1  was  sprayed  into  it,  the  sign  of  the  result  showing  that 
the  velocity  of  the  negative  ion  is  greater  than  that  of  the 
positive.  If  we  apply  the  preceding  formula  we  find,  on  the 
supposition  that  the  measurements  were  made  in  a  part  of  the 
flame  where  there  was  no  free  electricity,  that  the  difference 
between  the  velocities  of  the  negative  and  positive  ions  under  an 
electric  force  of  one  volt  per  centimetre,  i.e.  108  units,  would  vary 
from  2036  cm.  /sec.  for  the  pure  flame  to  740  cm.  /sec.  for  the 
flame  containing  the  concentrated  solution  ;  the  value  940  found 
by  H.  A.  Wilson  by  direct  experiment  is  between  these  limits. 

If  the  electric  and  magnetic  forces  are  considerable  there  will, 
when  there  is  no  escape  for  the  transverse  flow  of  ions,  be  very 
considerable  variations  in  the  number  of  ions  in  the  gas  :  for  putting 
2>!  =  Rm,  p2  =  Rn,  we  get  from  equations  (1)  and  (2), 

R  -j-  log  mn  =  eXH  (u  +  v), 


or  mn 

where  C  is  a  constant.  To  see  what  concentration  this  implies 
let  us  take  the  case  of  air  ionised  by  Rontgen  rays,  the  pressure 
being  1/1000  of  an  atmosphere,  then  since  u  +  v  at  atmospheric 
pressure  is  3  x  10-8crn./sec.,  at  the  assumed  pressure  it  will  be 
3  x  10-5,  and  if  X  is  10  volts  a  centimetre,  i.e.  109,  and  #=102, 
then  since  e/J?  =  4  x  10~7,  we  see 

mn  =  Cf€1'2z; 

*  Marx,  Drude's  Ann.  ii.  p.  798,  1900. 
T.  G.  U 


210  IONISATJON  IN   GASES   FROM   FLAMES.  [116 

thus  in  the  space  of  a  centimetre  parallel  to  z,  run  will  about  triple 
in  value :  this  variation  in  the  number  of  ions  will  affect  the 
distribution  of  the  current  parallel  to  x,  the  current  will  be 
greatest  where  there  are  most  ions  and  will  therefore  no  longer 
be  independent  of  z :  this  variation  in  the  current  may  affect  the 
distribution  of  potential  between  the  electrodes  and  thus  introduce 
fresh  sources  of  disturbance  into  the  problem. 

In  the  case  when  there  are  only  ions  of  one  sign  present,  say 
the  negative,  there  is  a  very  simple  solution  of  the  preceding  equa- 
tions, for  we  see  that  Z  =  eHXv,  p2  constant  and  X  the  same  as 
when  there  is  no  magnetic  force  satisfies  these  equations. 

Maximum  current  that  can  be  carried  by  the  vapour  of  a  salt. 

116.  H.  A.  Wilson*  has  made  an  exceedingly  important  set 
of  experiments  on  the  maximum  current  that  can  be  carried  by  a 
given  amount  of  salt  vapour ;  in  these  experiments  the  solution 
containing  the  salt  vapour  was  not  sprayed  into  flame,  but  into 
air  heated  by  passing  through  a  long  platinum  tube  raised  to 
bright  yellow  heat  by  a  furnace ;  a  smaller  central  tube  was 
placed  along  the  axis  of  the  outer  tube  and  the  current  between 
the  inner  and  outer  tubes  measured.  When  solutions  of  the 
strength  I/ 10th  normal  were  sprayed  and  the  temperature  of  the 
tubes  raised  and  the  potential  difference  increased,  a  stage  was 
reached  when  neither  an  increase  in  the  temperature  nor  in  the 
potential  difference  produced  any  increase  in  the  current.  Wilson 
measured  this  limiting  current  and  found  that  it  was  equal  to  the 
•current  which  when  passing  through  an  aqueous  solution  of  the 
salt  would  electrolyse  in  one  second  the  same  quantity  of  salt  as 
was  sprayed  in  that  time  into  the  hot  air ;  thus  if  the  salt  had 
been  supplied  to  water  at  the  same  rate  as  it  was  supplied  to 
the  hot  air  the  maximum  current  that  could  be  sent  through 
the  aqueous  solution  would  be  the  same  as  that  which  could  be 
sent  through  the  air;  this  was  proved  for  the  following  salts  of 
the  alkali  metals:  CsCl,  CsCO3,  Rbl,  RbCl,  Rb2COs,  KI,  KBr, 
KF,  K.C03,  Nal,  NaBr,  NaCl,  Na2CO3,  Lil,  LiBr,  LiCl,  Li2C03. 

*  H.  A.  Wilson,  Phil.  Mag.  vi.  4,  p.  207,  1902. 


CHAPTER    X. 

IONISATION  BY  LIGHT.     PHOTO-ELECTRIC  EFFECTS. 

THE  discovery  by  Hertz*  in  1887  that  the  incidence  of  ultra- 
violet light  on  a  spark  gap  facilitated  the  passage  of  the  spark, 
led  immediately  to  a  series  of  investigations  by  Hallwachsf, 
HoorJ,  Righi§  and  Stoletow||  on  the  effect  of  light,  and  especially 
of  ultra-violet  light,  on  charged  bodies.  It  was  proved  by  these 
investigations  that  a  newly  cleaned  surface  of  zinc,  if  charged  with 
negative  electricity,  rapidly  loses  this  charge  however  small  it  may 
be  when  ultra-violet  light  falls  upon  the  surface;  while  if  the 
surface  is  uncharged  to  begin  with,  it  acquires  a  positive  charge 
when  exposed  to  the  light,  the  negative  electrification  going  out 
into  the  gas  by  which  the  metal  is  surrounded ;  this  positive 
electrification  can  be  much  increased  by  directing  a  strong  air- 
blast  against  the  surface.  If  however  the  zinc  surface  is  positively 
electrified  it  suffers  no  loss  of  charge  when  exposed  to  the  light : 
this  result  has  been  questioned,  but  a  very  careful  examination 
of  the  phenomenon  by  Elster  and  GeitellF  has  shown  that  the 
loss  observed  under  certain  circumstances  is  due  to  the  discharge 
by  the  light  reflected  from  the  zinc  surface  of  negative  electrifica- 
tion on  neighbouring  conductors  induced  by  the  positive  charge, 
the  negative  electricity  under  the  influence  of  the  electric  field 
moving  up  to  the  positively  electrified  surface. 

*  Hertz,  Wied.  Ann.  xxxi.  p.  983,  1887. 

t  Hallwachs,  Wied.  Ann.  xxxiii.  p.  301,  1888. 

$  Hoor,  Repertorium  des  Physik,  xxv.  p.  91,  1889. 

§  Kighi,  G.  R.  cvi.  p.  1349 ;  cvii.  p.  559,  1888. 

||  Stoletow,  C.  R.  cvi.  .pp.  1149,  1593;  cvii.  p.  91;  cviii.  p.  1241;  Physikalische 
Revue,  bd.  i.,  1892. 

IT  Elster  and  Geitel,  Wied.  Ann.  xxxviii.  pp.  40,  497,  1889;  xli.  p.  161,  1890; 
xlii.  p.  564,  1891;  xliii.  p.  225,  1892;  lii.  p.  433,  1894;  Iv.  p.  684,  1895. 

14—2 


212  IONISATION  BY   LIGHT.  [116 

The  ultra-violet  light  to  produce  these  effects  may  be  obtained 
from  an  arc  lamp,  or  by  burning  magnesium,  or  by  sparking  with 
an  induction  coil  between  zinc  or  cadmium  terminals,  the  light 
from  which  is  very  rich  in  ultra-violet  rays.  Sunlight  is  not  rich 
in  ultra-violet  rays,  as  these  have  been  absorbed  by  the  atmosphere, 
and  it  does  not  produce  nearly  so  large  an  effect  as  the  arc-light. 
Elster  and  Geitel  who  have  investigated  with  great  success  the 
effects  produced  by  light  on  electrified  bodies  have  shown  that 
the  more  electropositive  metals  lose  negative  charges  even  when 
exposed  to  ordinary  daylight.  They  found  that  amalgams  of 
sodium  or  potassium  enclosed  in  a  glass  vessel  lose  a  negative 
charge  in  the  daylight,  though  the  glass  would  stop  any  small 
quantity  of  ultra-violet  light  that  might  be  left  in  the  light  after 
its  passage  through  the  atmosphere.  When  sodium  or  potassium 
by  themselves  instead  of  their  amalgams  were  used,  or,  what  is  more 
convenient  for  many  purposes,  the  liquid  alloy  formed  by  mixing 
these  metals  in  the  proportion  of  their  combining  weights,  they 
found  that  the  negative  electricity  was  discharged  by  the  light 
from  a  petroleum  lamp :  while  with  the  still  more  electropositive 
metal  rubidium  the  negative  electricity  could  be  discharged  by 
the  light  from  a  glass  rod  just  heated  to  redness.  They  found, 
however,  that  the  eye  was  more  sensitive  to  the  radiation  than 
the  rubidium,  for  no  discharge  could  be  detected  until  after  the 
radiation  from  the  glass  rod  was  visible. 

Elster  and  Geitel  arrange  the  metals  in  the  following  order 
with  respect  to  their  power  of  discharging  negative  electricity : 

Rubidium. 
Potassium. 

Alloy  of  Potassium  and  Sodium. 
Sodium. 
Lithium. 
Magnesium. 
Thallium. 
Zinc. 

For  copper,  platinum,  lead,  iron,  cadmium,  carbon,  and  mer- 
cury  the  effects  with  ordinary  light  are  too  small  to  be  measurable. 
The  order  of  the  metals  for  this  effect  is  the  same  as  in  Volta's 
series  for  contact-electricity,  the  most  electropositive  metals 


117]  PHOTO-ELECTRIC   EFFECTS/  213 

giving  the  largest  photo-electric  effect.  Many  substances  besides 
metals  discharge  negative  electricity  under  the  action  of  ultra-] 
violet  light:  lists  of  these  substances  will  be  found  in  papers  by) 
G.  C.  Schmidt*  and  O.  Knoblauch  f.  Among  the  more  active 
photo-electric  solids  are,  fluor-spar,  the  various  coloured  varieties 
of  which  vary  greatly  in  the  degree  to  which  they  possess  this 
property ;  the  sulphides  of  antimony;  lead,  arsenic,  manganese, 
silver,  and  tin  (the  sulphates  do  not  possess  this  property); 
hydroxide  of  tin,  iodide  of  lead,  many  aniline  dyes  in  the  solid 
state. 

Pure  water  is  not  photo-electric,  and  a  thin  film  of  water  over  - 
the  surface  of  a  metal  destroys  the  effect  due  to  the  metal.     The 
solutions   of  many  substances  are  however   very   photo-electric, 
especially    solutions   of    fluorescent   substances    such    as    eosine,   |^ 
fuchsine,  cyanine,  hydrochinone,  congo-red ;  potassium  nitrate  and 
formic  acid  also  show  this  effect.     Among  well-known  substances 
which  do  not  show  this  effect  we  may  mention  solutions  of  sulphate 
of  quinine,  potassium  permanganate  and  phenol. 

Photo-electric  properties  of  gases. 

117.  With  gases  the  action  of  light  may  be  expected  to  mani- 
fest itself  in  a  different  way  from  that  occurring  in  the  case  of  solids 
and  liquids,  we  cannot  expect  to  get  a  separation  of  electricity 
of  such  a  kind  that  one  region  of  the  gas  becomes  positively, 
another  negatively,  electrified.  If  a  molecule  of  a  gas  loses, 
like  a  piece  of  metal,  negative  electricity  when  exposed  to  ultra- 
violet light,  then  this  molecule  will  behave  like  a  positive  ion,  and 
the  negative  corpuscle  it  has  lost  will  attach  itself  to  some  other 
molecule  of  the  gas  which  will  act  like  the  negative  ion ;  thus  if  , 
ultra-violet  light  produced  on  the  molecules  and  atoms  of  a  gas  ) 
the  same  effect  as  it  does  on  a  mass  of  metal  we  should  expect  J 
this  effect  to  show  itself  as  ionisation  of  the  gas.  In  the  case  of 
sodium  vapour,  light  produces  a  decided  increase  in  the  conduc- 
tivity; it  is  not  necessary  that  the  light  should  be  ultra-violet,  the 
light  from  a  petroleum  lamp  is  sufficient  to  produce  well-marked 
effects ;  we  have  seen  that  sodium  when  in  the  solid  state  is 

•   G.  C.  Schmidt,  Wied.  Ann.  Ixiv.  p.  708,  1898. 

1   O.  Knoblauch,  Zeit.  /.  Physikalische  Chemie,  xxix.  p.  527,  1899. 


214  IONISATION   BY   LIGHT.  [117 

peculiarly  sensitive  to  the  action  of  light.  Experiments  have  been 
made  on  other  gases;  thus  Henry*  who  tried  the  effect  of  ultra- 
violet light  on  iodine  vapour,  which  absorbs  a  good  deal  of  light, 
could  not  detect  any  increase  in  conductivity  when  the  gas  was 
illuminated  :  Buissonf  was  unable  to  detect  any  conductivity  in  air 
through  which  ultra-violet  light  was  passing  :  recently,  however, 
Lenard  j  has  described  an  effect  due  to  a  very  easily  absorbed 
kind  of  ultra-violet  light  produced  when  sparks  from  an  induction 
coil  pass  between  aluminium  terminals ;  this  light  is  so  easily 
absorbed  by  air  that  its  effect  becomes  inappreciable  after  it  has 
passed  through  a  few  centimetres  of  air  at  atmospheric  pressure. 
Quartz  is  more  transparent  than  air  to  this  light ;  coal-gas, is  very 
much  less  transparent  than  air,  while  hydrogen  is  more  so.  If 
the  aluminium  terminals  were  placed  behind  a  quartz  window 
in  a  metal  plate,  then  a  charged  conductor  placed  on  the  far  side 
of  the  plate  near  to  the  gas  illuminated  by  these  rays  was  found 
to  lose  its  charge  rapidly  if  positively  electrified,  very  much  more 
slowly  if  negatively  electrified.  In  order  to  avoid  spurious  effects 
due  to  the  light  falling  on  metal  surfaces  in  the  neighbourhood 
Lenard  covered  these  with  soap  and  water,  which  he  found  pre- 
vented any  discharge  of  electricity  due  to  light  falling  on  a  metal 
plate.  The  much  greater  loss  experienced  by  the  plate  when  the 
charge  was  positive  than  when  it  was  negative  indicates  that  the 
velocity  of  the  negative  ions  is  much  greater  than  that  of  the 
positive.  Lenard  measured  by  a  method  used  by  Zeleny  and 
described  on  p.  38,  the  velocities  of  the  ions;  he  found  that 
under  a  potential  gradient  of  a  volt  per  centimetre  the  velocity 
of  the  negative  ions  through  air  at  atmospheric  pressure  is  3'13 
cm. /sec. :  this  is  considerably  greater  than  (almost  double)  the 
velocity  found  by  Rutherford  for  the  negative  ions  produced  by 
ordinary  ultra-violet  light  incident  on  a  metal  plate :  the  velocity 
of  the  positive  ions  was  found  by  Lenard  for  a  gradient  of  a  volt 
per  centimetre  to  be  only  '0015  cm. /sec.,  that  is  only  about  1/2000 
of  the  velocity  of  the  negative  ions.  The  exceedingly  small  velocity 
of  these  positive  ions  raises  the  question  as  to  whether  they  are 
not  particles  of  dust  or  minute  drops  of  impure  water,  rather  than 

'    *  Henry,  Proc.  Camb.  Phil.  Soc.  ix.  p.  319,  1897. 

f  Buisson,  quoted  by  Perrin,  Ann.  de  Chimie  et  de  Physique,  vii.  11,  p.  526, 
1897. 

J  Lenard,  Drude's  Ann.  i.  p.  486 ;  iii.  p.  298,  1900. 


117]  PHOTO-ELECTRIC   EFFECTS.  215 

gaseous  ions.  It  is  essential  to  show  that  they  are  not  of  this 
nature  if  these  experiments  are  to  demonstrate  the  ionisation  of  the 
air  by  the  ultra-violet  light,  for  the  enormous  discrepancy  between 
the  velocities  of  the  positive  and  negative  ions  is  exactly  what  we 
should  expect  if  dust  possessing  photo-electric  properties  were 
exposed  to  the  influence  of  ultra-violet  light;  such  particles  would 
emit  negative  electricity,  while  the  positive  electricity  would 
remain  behind  on  the  dust ;  the  comparatively  large  dust  particles 
would  move  very  slowly  in  an  electric  field,  while  the  negative 
ions  being  free  from  dust  might  be  expected  to  move  with  much 
greater  velocity.  Lenard  discusses  this  interpretation  of  his 
results  and  rejects  it  for  reasons  which  do  not  appear  to  us  abso- 
lutely convincing.  He  considers  that  the  negative  ions  produced 
by  the  action 'of  ultra-violet  light  on  air  are  essentially  different 
from  those  produced  when  the  light  falls  on  a  metal,  and  that 
while  the  latter  are  able  to  produce  condensation  in  a  steam  jet, 
the  former  are  unable  to  do  so.  The  evidence  for  this  is  as  follows ; 
though  the  gas  under  direct  illumination  by  the  ultra-violet  light 
produces  vigorous  condensation  in  a  steam  jet,  yet  if  the  negative 
ions  are  pulled  out  of  the  illuminated  gas  by  a  positively  charged 
plate  placed  at  some  distance  away  no  condensation  of  the  jet  takes 
place  in  the  region  between  the  plate  and  the  gas  exposed  to  the 
light,  though  the  leak  of  positive  electricity  from  the  plate  shows 
that  this  region  is  being  traversed  by  negative  ions.  To  make 
the  experiment  conclusive,  however,  we  require  to  know  the 
sensitiveness  of  the  steam  jet,  i.e.,  the  minimum  number  of  ions 
per  cubic  centimetre  it  is  capable  of  detecting,  and  also  to  be  sure 
that  the  number  of  negative  ions  in  the  neighbourhood  of  the  jet 
exceeds  this  minimum :  now  the  second  point  is  one  that  requires 
very  careful  attention,  for  if  the  electric  field  in  the  neighbourhood 
of  the  plate  is  intense  the  negative  ions  will  be  moving  at  a  very 
high  speed  and  a  very  small  number  of  ions  in  each  cubic  ceniii- 
metre  would  be  sufficient  to  produce  a  very  appreciable  leak ;  in 
fact  if  this  leak  is  '  saturated '  we  see  that  the  density  of  the  ions 
will  be  inversely  proportional  to  the  strength  of  the  field,  so  that 
by  increasing  this  strength  sufficiently  we  could  certainly  stop  the 
condensation  of  the  steam-jet.  Thus  this  experiment  does  noti. 
prove  that  the  negative  ions  are  incapable  of  acting  as  centres 
of  condensation  :  to  make  the  proof  valid  we  should  require  to 
know  that  the  number  of  ions  in  each  unit  volume  was  so  large 


216  IONISATION   BY   LIGHT.  [118 

that  condensation  would  take  place  if  these  ions  had  the  property 
of  the  normal  negative  ion. 

118.  C.  T.  R.  Wilson*  has  studied  the  action  of  ultra-violet 
light  on  gases  from  the  point  of  view  of  the  effect  produced  by  the 
light  on  the  formation  of  clouds.  His  results  with  intense  light 
have  already  been  described  in  Chapter  VII.,  we  shall  only  consider 
here  the  effects  he  got  with  very  feeble  light,  as  the  effects  have  a 
direct  bearing  on  the  question  of  the  ionisation  of  air  by  ultra- 
violet light,  though  they  do  not  touch  the  question  as  to  the  effects 
produced  by  the  extremely  absorbable  light  studied  by  Lenard. 
Wilson  found  that  with  very  feeble  ultra-violet  light  clouds  were 
produced  by  expansion  when  this  exceeded  a  definite  amount,  just 
as  in  the  case  of  a  gas  ionised  by  Rontgen  rays,  and  that  the 
amount  of  expansion  required  was  just  the  same  for  the  ultra- 
violet light  as  for  these  rays  :  this  at  first  sight  looks  as  if  the 
ultra-violet  light  ionised  the  gas.  Wilson,  however,  found  that  the 
clouds  produced  by  ultra-violet  light  differed  from  those  produced 
by  Rontgen  rays,  inasmuch  as  the  former  were  not  affected  by 
strong  electric  fields,  whereas  the  formation  of  the  latter  was 
almost  entirely  prevented  by  such  fields.  If  the  clouds  due  to 
ultra-violet  light  had  been  due  to  the  ionisation  of  the  gas  the 
ions  would  have  been  removed  by  the  field  and  the  clouds  stopped. 
At  the  same  time  the  coincidence  between  the  expansions  required 
for  the  formation  of  clouds  under  ultra-violet  light  and  when  ions 
are  present  is  so  remarkable  that  it  makes  us  very  reluctant  to 
believe  that  the  nuclei  are  different  in  the  two  cases ;  it  seems  to 
me  tfyat  an  explanation  which  is  in  harmony  with  the  facts  is  that 
charged  ions  do  form  the  nuclei  of  the  drops  formed  by  weak 
ultra-violet  light,  but  that  these  ions  are  produced  during  the 
expansion  of  the  gas  and  are  not  present  when  the  gas  is  at  rest; 
these  ions  might  arise  in  the  following  way :  we  have  seen  in 
Chapter  VII.  that  under  the  action  of  strong  ultra-violet  light  visible 
clouds  are  formed  without  expansion,  these  clouds  being  probably 
due  to  the  formation  of  hydrogen  peroxide,  which  mixing  with  the 
water  lowers  the  vapour  pressure;  now  when  the  light  is  very 
feeble  it  seems  probable  that  there  may  still  be  a  formation  of 
drops  of  water  which,  however,  in  consequence  of  the  very  small 
amount  of  hydrogen  peroxide  produced  by  the  feeble  light,  never 

*  C.  T.  R.  Wilson,  Phil.  Trans.  192  A,  p.  403,  1899. 


119]  PHOTO-ELECTRIC   EFFECTS.  217 

grow  large  enough  to  be  visible.  Thus  we  may  regard  the  air 
exposed  to  the  ultra-violet  light  as  full  of  exceedingly  minute 
drops  of  water ;  when  the  expansions  take  place  the  air  will  rush 
violently  past  the  drops  and  we  get  a  state  of  things  which  in 
many  respects  is  analogous  to  the  bubbling  of  gas  through  water; 
when,  however,  air  bubbles  through  water  there  is  as  Lord  Kelvin* 
has  shown  negative  electricity  in  the  air  and  positive  in  the  water; 
thus  when  the  air  rushes  past  the  water  drops  we  should  expect 
the  air  to  contain  negative  ions,  the  positive  ions  being  on  the 
drops;  the  ions  once  formed  would  act  as  nuclei  for  clouds  if  the 
expansion  exceeded  the  value  1*25.  If  this  view  is  correct,  then 
we  should  expect  the  number  of  ions  produced  by  an  expansion 
greater  than  1'25  to  increase  with  the  expansion,  for  in  this  case 
the  expansion  has  to  produce  the  nuclei  as  well  as  deposit  the 
clouds,  and  the  more  vigorous  the  expansion  the  greater  would  be 
the  number  of  nuclei  produced. 

It  is  an  important  meteorological  question  as  to  whether  direct 
sunlight  can  produce  a  cloud  in  the  atmosphere  without  expan- 
sion. Wilson  was  not  able  to  get  a  cloud  in  a  closed  vessel  in 
sunlight  with  less  than  the  normal  expansion  T25.  He  points 
out,  however,  that  the  conditions  in  the  open  air  are  more  favour- 
able to  the  production  of  clouds  than  those  in  a  closed  vessel,  for  in 
a  closed  vessel  the  drops  might  diffuse  to  the  sides  before  they  had 
time  to  grow  to  a  visible  size,  while  in  the  atmosphere  this  way  of 
escape  would  not  be  open  to  them. 

Photo-electric  effects  involve  an  absorption  of  Light. 

119.  Stoletowf  at  an  early  stage  in  the  history  of  this  subject 
called  attention  to  the  connection  between  the  photo-electric 
effects  and  the  absorption  of  the  ultra-violet  light ;  he  pointed 
out  that  water  which  does  not  give  photo-electric  effects  does  not 
absorb  many  of  the  visible  or  ultra-violet  rays,  while  solutions 
such  as  those  of  methyl -green  or  violet,  which  are  photo-electric, 
show  strong  absorption.  Hallwachs^:,  who  investigated  the  subject 
in  greater  detail,  showed  that  all  the  photo-electric  liquids  which 
he  tried  showed  strong  absorption  for  the  ultra-violet  light,  but 

*  Lord  Kelvin,  Proc.  Roy.  Soc.  Ivii.  p.  335,  1894. 
t  Stoletow,  Physikalische  Revue,  bd.  i.  1892. 
J  Hallwachs,  Wied.  Ann.  xxxvii.  p.  666,  1889. 


218 


IONISATION   BY  LIGHT. 


[119 


that  strong  absorption  was  not  always  accompanied   by  photo- 

?  electric  effects ;  thus  for  example  the  aqueous  solution  of  fuchsine 

/  is  photo-electric,  while  the  alcoholic  solution  is  not,  and  yet  the 

S  alcoholic  solution  absorbs  more  ultra-violet  light  than  the  aqueous 

>  one. 

The  effects  of  increased  absorption  are  shown  in  a  very 
beautiful  way  by  the  experiments  of  Elster  and  Geitel*  on  the  leak 
of  negative  electricity  from  surfaces  of  sodium,  potassium,  and 
rubidium  under  different  coloured  lights.  The  experiments,  the 
results  of  which  are  shown  in  the  following  table,  were  made  as 
follows ;  the  rate  of  escape  from  the  three  metals  when  exposed  to 
the  white  light  from  a  petroleum  lamp  was  measured,  these  mea- 
surements are  given  in  the  table  under  the  heading  '  white  light.' 
The  light  from  this  lamp  was  then  sent  through  an  ammoniacal 
solution  of  copper  oxide  and  the  metals  exposed  to  the  blue  light 
thus  obtained ;  this  solution  was  replaced  by  one  of  potassium 
chromate  to  get  yellow  light,  by  one  of  potassium  bichromate  to  get 
orange  light,  and  by  a  plate  of  deep  red  glass  to  get  the  red  light. 


Colour  of  Light 

Rate  of  leak  of  negative  electricity 

Na 

K 

Rb 

White 

21-0 

7'8 
226 
8-2 
21-9 
3'1 
21-9 
•2 

53-1 
30-3 
52-9 
3-5 
53-9 
2-2 
52-9 

o-i 

537-0 
86-8 
527-7 
339-7 
552-3 
182-0 
527-7 
21-0 

Blue  

White  

Yellow  

White      

Orange    . 

White  

Red  

Thus  we  see  from  this  table  that  though  for  white  and  blue 
lights  potassium  is  much  more  photo-electric  than  sodium,  it  is 
much  less  so  for  yellow  and  orange  light,  owing  to  the  strong  ab- 
sorption of  these  rays  by  the  sodium.  The  very  great  sensitiveness 
of  rubidium  to  light  of  long  wave-length  is  another  instance. 
Thus  while  the  ratios  of  the  leaks  for  rubidium  and  potassium 
under  blue  light  were  only  3  to  1,  the  ratio- for  yellow  light  was 
about  100  to  1. 

*  Elster  and  Geitel,  Wied.  Ann.  lii.  p.  433,  1894. 


120] 


PHOTO-ELECTRIC  EFFECTS. 


219 


Connection  between  the  rate  of  leak  and  strength  of  Electric  Field. 

120.  The  first  measurements  on  this  subject  were  made  by 
Stoletow*,  who  used  the  following  arrangement:  the  light  from 
an  arc  lamp  passed  through  a  hole  in  a  metal  screen,  and  after 
passing  through  a  perforated  plate  C  fell  upon  a  parallel  metal 
plate  D  ;  these  plates  were  connected  together  through  a  battery, 
the  negative  pole  of  the  battery  being  connected  with  D,  the  plate 
illuminated  by  the  light.  The  current  passing  between  the  plates 
was  measured  by  a  very  sensitive  galvanometer.  By  means  of  this 


E-5  10  15  20  25  3O   40    50   60    70    80   90  1OO 


Fig.  55. 

arrangement  Stoletow  measured  the  relation  between  the  current 
and  the  potential  difference  between  the  plates,  making  experi- 

*  Stoletow,  Journal  de  Physique,  ii.  9,  p.  468,  1890. 


220  IONISATION   BY   LIGHT.  [120 

ments  with  the  plates  at  distances  apart  varying  from  about  2*5 
millimetres  to  100  millimetres;  the  results  of  these  experiments,  in 
which  the  gas  between  the  plates  was  air  at  atmospheric  pressure, 
are  represented  by  the  curves  of  Fig.  55 ;  the  abscissae  represent 
the  potential  differences  between  the  plates,  the  unit  being 
1*43  volts  (the  electromotive  force  of  a  Clark's  cell);  the  ordinates 
represent  the  current  passing  between  the  plates,  the  unit  being 
8'6  x  10~u  amperes;  the  symbol  on  the  curve,  for  example  x+  25, 
indicates  that  the  distance  between  the  plates  was  x  4-  25  milli- 
metres, where  x  is  a  small  distance,  about  1*5  mm.,  that  was  not 
very  accurately  determined;  the  diameter  of  the  plates  was  22  mm. 
An  inspection  of  the  curves  shows  that  when  the  distance  between 
the  plates  is  small  and  the  electromotive  force  large  the  current 
increases  much  more  slowly  than  the  electromotive  force ;  it  is, 
however,  evidently  far  from  saturation ;  while  when  the  plates 
were  separated  by  distances  greater  than  25  mm.  there  was  no 
approach  to  saturation.  The  curves  corresponding  to  the  greater 
distances  between  the  plates  show  that  under  small  electromotive 
forces  the  current  increases  more  rapidly  than  the  potential  differ- 
ence. As  far  as  the  measurements  represented  in  the  figure  go 
i  is  approximately  the  same  at  all  distances  d,  provided  V/d  is 
the  same,  V  being  the  potential  difference,  i.e.,  i  is  a  function 
of  the  mean  value  of  the  electric  force  between  the  plates ;  this 
law,  as  Stoletow  showed  in  a  later  paper*,  does  not  apply  for  any 
great  range  of  potential  differences,  at  lower  pressures  especially 
the  departures  from  it  are  soon  very  apparent. 

Since  in  this  case  the  ions  are  all  of  one  kind  we  may  apply 
the  equation  of  Art.  99,  i.e., 

7*        Y  2  _L  8?n^ 

X  =  X°  +  ~IT> 

where  R  is  the  velocity  of  the  ion  under  unit  electric  force, 
i  the  intensity  of  the  current,  X0  and  X  the  values  of  the  electric 
force  at  the  plate  and  at  a  point  distant  x  from  it. 

To  form  an  estimate  of  the  variation  in  the  electric  field  which 
is  produced  by  the  presence  of  the  negative  ions  between  the 
plates,  let  us  take  one  of  Stoletow's  experiments  in  which  under  an 
electric  field  of  150  volts  per  cm.  the  current  was  3*3  x  10~~n 

*  Stoletow,  Journal  de  Physique,  ii.  9,  p.  469,  1890. 


120] 


PHOTO-ELECTRIC   EFFECTS. 


221 


amperes.  The  velocity  of  the  negative  ions  produced  by  a  field 
of  1  volt  per  centimetre  has  been  shown  by  Rutherford  to  be  about 
1'5  cm. /sec.  Hence  using  electrostatic  units,  X  and  X0  being 
the  values  of  X  at  places  a  centimetre  apart,  putting  i  =  10"1, 
^  =  4'5xl02,  X+X0=1,  in  the  preceding  equation,  we  get 
X  -  XQ=  1/180  or  a  little  less  than  2  volts  per  cm.,  thus  the 
variation  in  the  strength  of  the  field  is  comparatively  small. 
Stoletow,  who  determined  the  intensity  of  the  field  between  two 
parallel  plates  one  of  which  was  illuminated  by  ultra-violet  light, 
was  not  able  to  detect  any  variation  in  the  intensity.  Schweidler*, 
who  investigated  this  point  at  a  later  period,  found  that  the  distri- 
bution of  potential  between  the  plates  when  the  ultra-violet  light 
was  in  action,  was  not  quite  uniform ;  his  results  are  shown  in 
Fig.  56,  where  the  curved  line  represents  the  distribution  of 


/ 

/ 

i' 

l\ 

n 

/ 

i 

Ij 

n 

<; 

l 

~5 

/ 

/ 

/ 

1 

} 

/ 

/ 

1 

l 

I 

1 

/ 

1 

/ 

1 

/ 

) 

/ 

/ 

/ 

// 

1 

0     5    10  16    20  35  30  39  40  45  50  65 


Fig.  56. 

potential  when  the  light  was  shining,  the  straight  one  when  it 
was  not.  The  curvature  of  the  potential  curve  in  the  light  is  all 
in  one  direction,  indicating  the  presence  of  an  excess  of  negative 
ions  in  every  part  of  the  region  between  the  plates.  The  varia- 
tion in  the  intensity  of  the  field  between  the  plates  has  also  been 
observed  and  measured  by  Buissonf  and  used  by  him  to  determine 
the  velocity  of  the  negative  ions ;  he  finds  that  under  a  potential 
gradient  of  a  volt  per  cm.  this  velocity  is  about  2'2  cm./sec. 

*  Schweidler,  Wien.  Ber.  cvii.  p.  881,  1898. 

t  Buisson,  Comptes  Rendus,  cxxvii.  p.  224,  1898. 


222 


IONISATION   BY   LIGHT. 


[120 


Schweidler*  has  also  made  experiments  on  the  relation  between 
the  current  and  the  strength  of  the  electric  field  over  a  wider 
range  than  in  Stoletow's  experiments :  his  results  for  air  at  atmo- 
spheric pressure  are  shown  by  the  curve  (Fig.  57).  It  will  .be 


120 


no 


100 


10 


0   ,   1000    2000   3000    4000   5000 
Fig.  57. 


noticed  that  when  the  strength  of  the  field  approaches  the  value 
5730  volts,  which  is  the  strength  required  to  spark  across  the 
plates  which  were  3  mm.  apart  in  the  dark,  there  is  a  very  great 
increase  in  the  current. 

This  rapid  increase  of  the  photo-electric  effect  in  the  neigh- 
bourhood of  the  sparking  potential  was  first  observed  by  Kreusler^. 
The  relation  between  the  leak  from  plates  of  iron,  aluminium, 
copper,  zinc,  silver  and  amalgamated  copper,  and  the  strength  of 
field  are  represented  in  the  curves  given  in  Fig.  58 :  the  abscissae? 
measured  from  0  represent  the  difference  between  the  electromotive 
force  applied  and  that  required  to  produce  discharge  in  the  dark. 
The  increase  in  the  leak  is  so  great  that  it  cannot  be  adequately 


*  Schweidler,  Wien.  Ber.  cviii.  p.  273,  1899. 
t  Kreusler,  Drude's  Ann.  vi.  p.  398,  1901. 


120] 


PHOTO-ELECTRIC    EFFECTS. 


223 


represented  in  a  moderately  sized  figure,  a  better  idea  in  the  case 
of  the  zinc  plate  can  be  derived  from  the  following  table  given  by 


Fig.  58. 

Kreusler.      V  is  the  potential  difference  and  i  the  current,  the 
potential  required  to  produce  a  spark  was  4060. 


V 

i(l  =  10-10 
Amp.) 

V 

i(l  =  10-10 
Amp.) 

V 

i(l  =  10-10 
Amp.) 

4040 

13639 

3050 

0-19 

;       i 
3300      0-36 

3970 

25-67 

2540 

0-09 

3440      0-58 

3780 

5-88 

1760 

0-06 

3640      1-36 

3700 

2-40 

1170 

0-05 

3710      1-98 

3590 

1-39 

1760 

0-06 

3760      3-88 

3440 

070 

2530 

0-08 

3970     21-09 

3300 

0'40 

3060 

0-17 

4040      80-51 

These  figures  also  show  evidence  of  an  effect  often  observed 
when  using  ultra-violet  light — the  decrease  of  sensibility  with  the 
time ;  thus  of  the  two  readings  taken  with  the  greatest  potential 
difference  the  later  one  was  very  appreciably  less  than  the  earlier 


224 


IONISATION   BY  LIGHT. 


[120 


one.  This  '  fatigue  '  of  the  plates  is  probably  due  to  oxidation,  it 
does  not  take  place  in  hydrogen  nor  at  very  low  pressures,  nor 
when  platinum  is  used  instead  of  zinc. 

The  increase  in  the  rate  of  leak  when  the  electric  field  ap- 
proaches a  certain  strength  is  also  very  evident  when  the  gas  is  at 
lower  pressures.  The  etfect  of  altering  the  pressure  of  the  gas  was 
first  investigated  by  Stoletow*,  and  subsequently  by  Schweidler  f 
and  Lenardj.  Stoletow  showed  that  as  the  pressure  was  dimi- 
nished, starting  from  atmospheric  pressure,  the  current  slightly 
increased,  the  change  in  the  current  being  small  compared  with 
that  in  the  pressure  ;  on  carrying  the  reduction  of  pressure  still 
further,  a  stage  was  reached  (if  the  strength  of  the  field  was  not 
too  small)  when  the  current  increased  rapidly  as  the  pressure 
diminished,  this  went  on  until  the  current  reached  a  maximum 
value,  after  which  it  began  to  decline,  but  at  the  lowest  obtainable 
pressures  it  had  a  finite  value  which  was  independent  of  the 
strength  of  the  electric  field. 


100 


80 


60 


40 


20 


.  I  =o«83  mfm 


cL 


Fig.  59. 

The  variation  of  the  current  with  the  pressure  when  the 
potential  difference  remains  constant  is  exhibited  in  the  curves 
(copied  from  Stoletow's  paper)  shown  in  Fig.  59;  the  distance 

*  Stoletow,  Journal  de  Physique,  ii.  9,  p.  468,  1890. 
t  v.  Schweidler,  Wien.  Ber.  cviii.  p.  273,  1899. 
£  Lenard,  Drude's  Ann.  ii.  p.  359,  1900. 


120] 


PHOTO-ELECTRIC   EFFECTS. 


225 


between  the  plates  was  '83  millimetres  and  the  figures  on  the 
curves  indicate  the  potential  difference  expressed  in  terms  of 
Clark's  cells  (1  Clark's  cell  =  1-4  volts). 

The  values  of  the  current  at  a  series  of  pressures  when  the 
distance  between  the  plates  was  371  mm.  and  the  potential 
difference  about  90  volts  are  shown  in  the  following  table : 


Pressure  in 
millimetres 

Current 

Pressure  in 
1  millimetres 

Current 

Pressure  in 
millimetres 

Current 

754 

8-46 

2-48 

74-7 

0105 

65-8 

152 

13-6 

1-01 

105-8 

0-0147 

53-8 

21 

26-4 

0-64 

108-2 

0-0047 

50-7 

8-8 

32-2 

0-52 

102-4 

0-0031 

49-5 

3-3 

48-9 

0-275 

82-6 

We  see  by  an  inspection  of  the  curves  in  Fig.  59  that  the 
pressure  at  which  the  current  is  a  maximum  increases  with  the 
electric  force  between  the  plates  :  Stoletow  has  shown  that  pm, 
the  pressure  at  which  the  current  is  a  maximum,  is  proportional 
to  E/d,  where  d  is  the  distance  and  E  the  potential  difference 
between  the  plates;  this  law  may  also  be  expressed  by  saying  that  if 
X  is  the  mean  free  path  of  a  molecule  at  the  pressure  for  maximum 
current,  when  the  electric  force  is  X,  then  X\  is  constant.  The 
curves  in  Fig.  59  show  that  at  very  low  pressures  the  current 
is  independent  of  the  strength  of  the  electric  field,  i.e.  is 
saturated.  This  is  also  well  shown  by  the  following  numbers  taken 
from  Lenard's  paper.  V  is  the  potential  difference  in  volts  and  t 
the  current,  the  vacuum  was  the  best  obtainable,  the  pressure  being 
less  than  '002  mm.  of  mercury. 


V 

t 

V 

t 

45000 

24-5  x  10  ~10  Coulomb/sec. 

500 

23-4  x  10~  10  Coulomb/sec. 

25000 

26-6 

120 

21-9 

8900 

22-5 

14 

19-9        „ 

4100 

24-8 

9 

15-9 

3110 

24-5         , 

1 

7           „              » 

1300 

24-5 

0 

4 

The  critical  pressure  is  of  the  same  order  of  magnitude  as  the 
pressure  at  which  the  electric  field  would  be  able  to  produce  a 

15 


T.  G. 


226 


IONISATION   BY   LIGHT. 


[120 


discharge  in  the  dark ;  in  this  region  of  pressure  Stoletow  has 
shown  that  the  current  does  not  depend  merely  upon  the  value  of 
E/d  where  E  is  the  potential  difference  and  d  the  distance  between 
the  plates,  for  with  a  constant  value  of  E/d  the  current  at  these 
pressures  increases  rapidly  with  the  distance  between  the  plates. 

V.  Schweidler*  has  given  curves  representing  the  relation 
between  the  current  and  the  potential  difference  at  several 
pressures.  Similar  curves  have  lately  been  obtained  by  Varley  at 
the  Cavendish  Laboratory,  some  of  these  are  reproduced  in  Figs. 
60  and  61.  The  curves  show  three  distinct  stages ;  the  first  when 


& 


ISO 


160 


•> 

If  12° 

CO  »H 

S  '[  10° 

1  £ 
1=3 

JE. 

.S          60 


•8        40 

I 

«  20 


llmm 


33mm 


0     20    40    60    80    100   120    140    16O    180 

Potential  to  which  Zinc  is  charged  in  cells. 
1  cell  =  2-1  volts  (nearly). 

Fig.  60.    Variation  of  ultra-violet  light  leak  from  zinc  surface  with  the  pressure 
for  constant  illumination. 

The  experiments  were  conducted  in  hydrogen.     The  distance  between  the 
electrodes  was  1  cm. 

the  electric  force  is  weak,  then  the  current  increases  rapidly  with 
the  electric  force,  the  rate  of  increase  gradually  dies  away  as  the 


*  v.  Schweidler,  Wien.  Ber.  cviii.  p.  273,  1899. 


120] 


PHOTO-ELECTRIC   EFFECTS. 


227 


electric  force  increases,  and  the  second  stage  is  reached  when  the 
current  only  varies  slowly,  at  some  pressures  hardly  at  all,  with 
the  electric  field ;  with  still  larger  electric  forces  a  third  stage  is 


^  20° 

1 

'il    180 
g^  160 

o  140 

.2 

OJ 

a 


120 


100 


|  so 

1 

~    60 


20 


0.36  m  m 


0-  140mi 


0-074  mm 


0    044  m  m 


0-  021  m  m 


-0-013-m-m 


0-  008  mm 


20          40          60          80         100        120       140        160       180 

Potential  to  which  Zinc  is  charged  in  cells.     1  cell  =  2-1  volts  (nearly). 

Fig.  61.     Variation  of  ultra-violet  light  leak  from  zinc  surface  with  the  pressure, 
when  the  latter  is  low,  for  constant  illumination. 

The  experiments  were  conducted  in  air.    The  distance  between  the  electrodes 
was  4  mm. 

reached  when  the  current  increases  rapidly  with  the  electric  force 
and  also  with  the  distance  between  the  electrodes. 


15—2 


228  IONISATION   BY  LIGHT.  [121 

Theoretical  considerations  relating  to  the  connection   between  the 
current  and  the  strength  of  the  electric  field. 

121.  It  will  be  convenient  to  confine  our  attention  in  the  first 
place  to  electric  fields  which  are  weak  compared  with  those  required 
to  produce  discharge  in  the  dark.  The  view  we  take  of  the  action 
of  the  ultra-violet  light  is  that  under  the  action  of  this  light  the 
metal  emits  from  each  unit  area  in  unit  time  a  certain  number 
of  corpuscles;  that  these  soon,  when  gas  surrounds  the  metal, 
get  attached  to  one  or  more  molecules  of  the  gas  and  form 
negative  ions.  If  there  is  no  electric  field  to  remove  these  ions 
they  will  go  on  accumulating  in  front  of  the  metal  plate,  and  as 
the  number  of  the  ions  is  greater  at  a  little  distance  from  the 
plate  than  at  the  plate  itself,  there  will  be  diffusion  of  the  ions 
from  the  place  of  greater  to  the  place  of  less  density,  i.e.  back  into 
the  plate,  and  things  will  reach  a  steady  state  when  the  accumu- 
lation of  ions  in  front  of  the  plate  is  so  great  that  the  number  of 
ions  which  diffuse  back  into  the  plate  is  equal  to  the  number 
shot  from  it  by  the  ultra-violet  light.  If  an  electric  field  acts  on 
the  gas  some  of  the  ions  will  move  off  through  the  gas,  producing 
a  current  of  electricity ;  the  accumulation  of  ions  will  not  be  so 
great  as  in  the  previous  case,  and  equilibrium  will  be  reached 
when  the  number  of  ions  shot  off  by  the  ultra-violet  light  is  equal 
to  the  number  which  diffuse  back  into  the  plate  plus  the  number 
which  are  carried  away  by  the  electric  field. 

To  put  these  considerations  in  a  symbolical  form  let  us  take 
the  case  when  the  current  is  flowing  between  two  parallel  plates : 
let  /  be  the  number  of  negative  ions  emitted  *  by  unit  area  of  the 
illuminated  surface  in  unit  time,  and  <r  the  number  of  ions  per  c.c. 
at  any  point  between  the  plates,  then  if  X  is  the  electric  force,  it 
the  velocity  acquired  by  a  negative  ion  under  unit  electric  force, 
e  the  charge  on  an  ion,  and  i  the  current  flowing  through  unit 
area,  then  Xuo-e  —  i :  we  have  seen  that  X  is  approximately  con- 
stant between  the  plates,  hence  as  i  is  constant  it  follows  that  a- 
will  be  approximately  constant.  This  constant  value  of  cr  will 
not  however  hold  right  up  to  the  illuminated  plate,  we  may 
suppose  that  the  density  of  the  ions  increases  from  zero  to  this 

*  These  ions  start  as  corpuscles  but  are  soon  converted  into  ions  by  adhesion  to 
the  molecules  of  the  gas  surrounding  them. 


121]  PHOTO-ELECTRIC   EFFECTS.  229 

constant  value  in  a  small  distance  \  from  the  plate :  thus  at  the 
surface  of  the  plate  there  will  be  a  gradient  in  the  density  of  the 
ions  of  the  order  cr/X,  and  if  D  is  the  coefficient  of  diffusion  of  the 
ions  through  the  gas  the  number  of  negative  ioas  flowing  back 
into  unit  area  of  the  plate  in  unit  time  is  Da/\.  The  number  of 
ions  carried  away  through  the  gas  by  the  electric  field  in  unit 
time  is  i/e,  hence  we  have  when  things  have  settled  into  a  steady 
state, 

Da-     i 


but  Xuae  =  i,  hence  we  have 

/=- 
( 

e\XuI 


this  relation  between  i  and  X  exhibits  the  chief  features  of  the 
earlier  parts  of  the  curves  obtained  by  Schweidler  and  Stoletow  : 
when  X  is  small  the  current  is  proportional  to  the  electromotive 
force,  it  soon  however  increases  less  rapidly  than  X,  and  when  X 
is  very  large  approximates  to  the  constant  value  le. 

We  have  seen  (p.  32)  that  u  =  De  (n/p),  where  n  is  the  number 
of  molecules  in  a  cubic  centimetre  of  gas  at  the  pressure  p  :  thus 
•u/D  is  the  same  for  all  gases:  hence  we  see  from  (1)  that  any 
alteration  in  the  current  produced  by  altering  the  gas  thrpugh 
which  the  current  passes  must  be  due  to  the  alteration  in  X  :  so 
that  if  this  equation  were  rigorously  true  then  under  the  same 
potential  difference,  provided  this  were  small,  the  currents  through 
different  gases  would  be  proportional  to  the  values  of  X  for  these 
gases.  In  this  connection  it  is  necessary  to  remember  that  the 
diffusion  of  the  ions  back  into  the  metal  takes  place  through 
a  layer  of  gas  in  immediate  proximity  to  the  metal,  and  that  D 
refers  to  this  layer,  while  the  u  which  occurs  in  equation  (1) 
relates  to  the  gas  at  a  considerable  distance  away  from  the 
plate  ;  if  there  were  anything  in  the  nature  of  a  gaseous  layer 
adhering  to  the  metal,  then  the  gas  through  which  the  ions  diffuse 
might  be  different  from  the  gas  in  the  rest  of  the  field,  so  that 
we  should  not  be  justified  in  assuming  that  the  ratio  of  D  to 
u  was  a  constant  independent  of  the  nature  of  the  gas.  Again, 
we  have  assumed  that  the  only  ions  available  for  carrying  the 


230  IONISATION   BY   LIGHT.  [122 

current  are  those  which  come  out  of  the  metal :  now  we  shall  see 
directly  that  the  motion  of  ions  through  a  gas  with  a  high  velocity 
ionises  the  gas,  thus  if  the  corpuscles  are  projected  from  the 
metal  with  a  velocity  exceeding  a  certain  critical  value  they  will 
ionise  the  molecules  of  the  gas  against  which  they  strike,  and  thus 
the  total  number  of  ions  produced  would  exceed  the  number 
projected  from  the  metal  by  an  amount  depending  upon  the 
nature  of  the  gas.  The  observations  hitherto  made  on  different 
gases  are  not  sufficiently  extensive  to  enable  us  to  decide  whether 
or  not  an  effect  of  this  kind  does  exist*.  Elster  and  Geitelf  and 
StoletowJ  found  that  with  the  strength  of  electric  field  used  by 
them  the  rate  of  escape  of  electricity  through  carbonic  acid  gas 
was  much  greater  than  that  through  air  or  oxygen.  Breisig§  on 
the  contrary  found  that  the  rate  was  less  through  C02  than 
through  air:  and  that  it  was  exceptionally  large  through  the 
vapours  of  ether  and  alcohol.  The  rate  of  leak  varies  so  much 
with  the  potential  difference  that  a  comparison  of  the  rates  of 
leak  for  the  different  gases  with  only  one  value  for  the  potential 
difference  is  not  satisfactory  and  gives  little  information.  What 
is  really  wanted  is  a  comparison  for  the  different  gases  of  the 
curves  representing  the  relation  between  the  current  and  the 
potential  difference.  It  would  also  be  desirable  to  have  these 
curves  drawn  for  ultra-violet  light  of  different  wave-lengths. 
The  different  gases  might  also  cause  the  currents  to  differ  by 
altering  the  surface  of  the  metal  either  by  combining  with  it  or 
by  condensing  on  its  surface. 

122.  We  shall  now  go  on  to  consider  the  sudden  increase  in 
the  current  which  occurs  when  the  electric  field  approaches  the 
intensity  required  to  produce  a  discharge  in  the  dark.  We  can, 
I  think,  explain  this  by  means  of  some  considerations  first  advanced 
by  the  author ||  to  explain  the  ionisation  produced  when  a  strong 
electric  field  causes  a  discharge  to  pass  through  a  gas.  When 
cathode  or  Lenard  rays  pass  through  a  gas,  the  gas  becomes  a 

*  Since  this  was  written  Varley  has  made  at  the  Cavendish  Laboratory  experi- 
ments proving  the  existence  of  this  secondary  ionisation. 

t  Elster  and  Geitel,  Wied.  Ann.  xli.  p.  161,  1890. 

J  Stoletow,  C.  R.  cvii.  p.  91,  1888. 

§  Breisig,  Bonn.  Diss.  1891 ;  Wied.  Beiblatter,  xvii.  p.  60. 

||  J.  J,  Thomson,  Proc.  Camb.  Phil.  Soc.  Feb.  5,  1900;  Phil.  Mag.  v.  50, 
p.  278,  1900. 


122]  PHOTO-ELECTRIC   EFFECTS.  231 

conductor,  i.e.  it  is  ionised ;  hence  we  see  that  when  very  rapidly 
moving  ions  pass  through  a  gas  and  come  into  collision  with  its 
molecules  the  gas  is  ionised :  the  energy  required  for  the  ionisation 
coming  from  the  kinetic  energy  of  the  rapidly  moving  ions. 
Inasmuch  as  the  ionisation  of  a  molecule  of  a  gas  requires  the 
expenditure  of  a  finite  amount  of  work,  a  moving  ion  cannot 
ionise  a  molecule  against  which  it  strikes  unless  its  kinetic  energy 
exceeds  a  certain  critical  value,  but  when  its  energy  does  exceed 
this  value  then  a  certain  fraction  of  the  number  of  collisions 
between  the  ions  and  the  molecule  will  result  in  ionisation.  Now 
when  the  ions  are  moving  in  an  electric  field,  the  kinetic  energy 
acquired  by  the  ions  will  increase  as  the  strength  of  the  field 
increases,  and  when  the  field  is  strong  enough  to  make  the  kinetic 
energy  of  the  ions  exceed  the  critical  value,  the  ions  by  their 
collisions  will  give  rise  to  new  ions,  and  thus  there  will  be  an 
increase  both  in  the  number  of  ions  and  the  current  through  the 
gas:  it  is  this  increase  which  is  so  marked  a  feature  of  the 
currents  produced  by  ultra-violet  light  when  the  electric  field  is 
strong. 

If  I  is  the  mean  free  path  of  an  ion,  X  the  electric  force,  e  the 
charge  on  the  ion,  then  the  mean  kinetic  energy  given  to  the  ion 
by  the  electric  field  is  Xel ;  when  therefore  Xel  exceeds  a  certain 
critical  value,  ionisation  will  take  place  in  a  certain  fraction  of  the 
collisions ;  let  us  denote  this  fraction  by  f(Xel),  f(x)  being  a 
function  of  x  which  vanishes  when  x  is  less  than  a  certain  value. 
If  there  are  n  ions  per  cubic  centimetre,  then  the  number 
of  collisions  in  unit  time  is  equal  to  nv/l,  where  v  is  the  average 
velocity  of  translation ;  hence  the  number  of  ions  produced  in 

77?) 

unit  time  per  unit  volume  is  -j-f(Xel).     A  certain  number  of 

6 

collisions  may  result  either  in  the  recombination  of  the  ion,  or 
the  attachment  of  the  ion  to  the  system  against  which  it  collides, 
so  that  the  ion  ceases  to  be  available  for  carrying  the  current ;  let 
a  fraction  /3  of  the  collisions  result  in  the  destruction  of  the  ion  as 
an  ionising  agent,  then  the  number  of  these  ions  which  disappear 

from  a  cubic  centimetre  of  the  gas  in  unit  time  is  fi  -j-  *,  hence  the 

*  We  have  here  neglected  the  loss  of  ions  due  to  the  recombination  of  positive 
and  negative  ions  in  comparison  with  that  due  to  the  collision  of  the  ions  with  the 
molecules. 


232  IONISATION   BY   LIGHT.  [122 

excess  of  the  ions  produced  over  those  which  disappear  is  equal  to 


We  have  by  the  equation  of  continuity,  if  u  is  the  average 
velocity  of  translation  parallel  to  the  axis  of  x, 


Now  when  the  ions  are  moving  so  rapidly  that  they  have 
sufficient  kinetic  energy  to  act  as  ionising  agents,  their  velocity 
must  be  mainly  due  to  the  electric  field,  since  when  this  field  is 
absent  no  ionisation  is  produced.  Hence  we  have  approximately 

v  —  u. 
Hence  when  things  are  in  a  steady  state  we  have  by  (2) 


integrating  we  get 

„  } 

nu  =  Cel 
or  if  as  a  first  approximation  we  regard  X  as  constant  we  have 


If  the  current  has  reached  the  saturation  stage  before  ionisation 
begins,  then  nu  —  I  when  x  =  0  when  x  is  measured  from  the 
illuminated  plate,  hence 


T 

nu  =  Iel 

if  d  is  the  distance  between  the  plates,  then  i  the  current  is  the 
value  of  nue  when  x  =  d,  thus 


...........................  (3), 

thus  when  this  additional  ionisation  sets  in,  the  current  with  a 
constant  value  of  X  increases  with  the  distance  between  the 
plates  ;  this  effect  has  been  observed  by  Stoletow*.  As  long  as  the 
ionisation  is  confined  to  that  produced  at  the  metal  plate  by  the 
ultra-violet  light,  the  current  is  determined  by  the  electric  force, 
i.e.  i  is  a  function  of  X  and  not  of  d  ;  when  however  the  secondary 
ionisation  occurs  i  is  a  function  of  both  X  and  d. 

*  Stoletow,  Journal  de  Physique  [2],  ix.  p.  468,  1890. 


122]  PHOTO-ELECTRIC   EFFECTS.  233 

The  point  at  which  the  secondary  ionisation  begins  is  when 
Xel  has  a  certain  definite  value ;  as  I  the  mean  free  path  of  an  ion 
is  inversely  proportional  to  the  pressure,  the  value  of  X  required 
to  start  the  secondary  ionisation  will  be  directly  proportional  to 
the  pressure;  the  curves  given  by  v.  Schweidler*  for  the  relation 
between  the  current  and  electromotive  force  at  different  pressures 
show  that  his  experiments  are  in  fair  agreement  with  this  result, 
he  only  gives  approximate  values  for  the  pressures,  and  there 
are  hardly  sufficient  points  determined  on  the  curve  to  enable 
us  to  determine  with  accuracy  the  points  at  which  the  secondary 
ionisation  commences ;  but  from  an  inspection  of  his  curves 
I  should  say  that  at  a  pressure  of  750  mm.  secondary  ionisation 
began  when  the  difference  of  potential  between  his  plates,  whose 
distance  apart  is  given  as  between  3 — 5  mm.,  was  equal  to 
4700  volts,  at  130mm.  to  1150  volts,  and  at  17mm.  to  about 
140  volts. 

It  is  evident  that  the  current  cannot  go  on  continually  in- 
creasing as  the  pressure  diminishes,  for  in  the  limit  when  the  free 
path  gets  comparable  with  the  distance  between  the  plates  there 
will  be  very  few  collisions,  and  therefore  little  if  any  secondary 
ionisation  ;  in  the  limit  when  the  pressure  is  indefinitely  reduced, 
the  number  of  ions  reaching  the  plate  not  exposed  to  the  light 
must  equal  the  number  leaving  the  illuminated  plate,  hence 
with  our  previous  notation  the  limiting  current  will  be  equal 
to  le. 

The  value  of  the  free  path  at  the  pressure  when  the  current 
is  a  maximum  is  by  equation  (3)  determined  by  finding  the 
value  of  I  which  makes  {/  (Xel)  —  /3}/l  a  maximum,  this  condition 
gives  /'  (Xel)  Xel  —f  (Xel)  —  /3,  an  equation  to  determine  Xel ; 
thus  when  the  current  is  a  maximum  XI  has  a  constant  value, 
this  coincides  with  Stoletow's  result  that  if  pm  is  the  pressure 
at  which  the  current  is  a  maximum  X/pm  is  constant. 

We  alluded  before  to  the  question  as  to  whether  secondary 
ionisation  was  produced  close  to  the  surface  of  the  metal  by  the 
corpuscles  shot  out  from  the  metal  through  the  influence  of  the 
ultra-violet  light ;  it  would  seem  that  this  point  might  be  deter- 
mined by  careful  measurements  of  the  current  under  a  constant 

*  v.  Schweidler,  Wien.  Ber.  cvii.  p.  273,  1899. 


234  IONISATION   BY  LIGHT.  [123 

electromotive  force  at  different  pressures,  for  if  it  was  found  that 
the  current  before  secondary  ionisation  began  rose  to  a  value 
greater  than  that  corresponding  to  an  exceedingly  low  pressure,  it 
would  prove  that  such  secondary  ionisation  at  the  surface  of  the 
metal  did  occur.  In  Stoletow's  experiments  at  various  pressures 
the  current  before  secondary  ionisation  took  place  did  not  exceed 
the  value  at  zero  pressure,  this  point  however  is  one  that  would 
repay  further  examination*. 


The  Photo-electric  Effect  depends  upon  the  orientation  of  the  plane 
of  polarisation  of  the  Light. 

123.  Elster  and  Geitel  f  made  the  very  interesting  discovery 
that  when  the  incident  light  is  plane  polarised,  the  photo-electric 
effect,  the  intensity  and  angle  of  incidence  being  the  same,  is  greater 
when  the  light  is  polarised  at  right  angles  to  the  plane  of  incidence 
than  when  it  is  polarised  in  that  plane.  On  the  Electro-magnetic 
Theory  of  Light  there  is  in  light  polarised  at  right  angles  to  the  plane 
of  incidence  an  electric  force  with  a  component  normal  to  the  re- 
flecting surface,  when  the  light  is  polarised  in  the  plane  of  incidence 
the  electric  force  is  parallel  to  this  surface.  The  most  convenient 
way  of  investigating  the  effect  of  polarisation  is  to  use  a  liquid 
surface,  as  it  is  important  that  the  reflecting  surface  should  be 
smooth,  and  to  choose  a  liquid  which  is  sensitive  to  ordinary  light, 
as  it  is  then  possible  to  use  a  Nicols  prism  to  polarise  the  light : 
the  liquids  used  by  Elster  and  Geitel  were  the  liquid  alloy  of 
sodium  and  potassium,  and  amalgams  of  rubidium  and  caesium, 
these  were  placed  in  vessels  from  which  the  air  was  exhausted 
and  the  rate  of  escape  of  negative  electricity  observed  with  light 
incident  on  the  surfaces  at  different  angles.  Some  of  the  results 
obtained  in  this  way  are  given  below,  data  were  not  given  to 
enable  us  to  say  to  which  stage  of  the  curve  connecting  the  rate 
of  escape  of  negative  electricity  with  the  electromotive  force  the 
observations  refer. 


*  See  foot-note,  p.  230. 

t  Elster  and  Geitel,  Wied.  Ann.  lii.  p.  433,  1894;  Iv.  p.  684,  1895;  Ixi.  p.  445, 
1897. 


123] 


PHOTO-ELECTRIC   EFFECTS. 


235 


Rate  of  escape  (t)  of  electricity  from  sodium  potassium  amal- 
gam exposed  to  white  light  polarised  at  right  angles  to  the  plane  of 
incidence. 


Angle  of 
incidence 

t 

Angle  of 
incidence 

i 

Angle  of 
incidence 

i 

o 

0 

2-8 

o 

30 

17-4 

60° 

28-7 

10 

5-2 

40 

23-4 

70 

23-8 

20 

11-2 

50 

27-0 

80 

11-0 

Rate  of  escape  (i)  of  electricity  from  the  same  cell  exposed  to 
white  light  polarised  in  the  plane  of  incidence. 


Angle  of 
incidence 

i 

Angle  of 
incidence 

i 

Angle  of 
incidence 

i 

o 

3 

10 

20 

2-8 
2-78 
2-87 

o 

30 

40 
50 

2-65 
2-24 
1-80 

o 

60 

70 
80 

1-51 
1-01 
•33 

Thus,  except  at  perpendicular  incidence  when  the  two  are 
necessarily  equal,  the  leak  caused  by  the  light  polarised  in  the 
plane  of  incidence  is  very  much  smaller  than  that  caused  by  light 
polarised  at  right  angles  to  this  plane,  and  we  see  too  that 
whereas  in  the  former  case  the  current  continually  diminishes  as 
the  angle  of  incidence  increases,  in  the  latter  it  increases  with 
the  angle  of  incidence  until  the  latter  is  about  60°,  after  this  the 
current  decreases. 

Elster  and  Geitel  have  determined  how  the  amount  of  light 
absorbed  by  the  metal  varies  with  the  angle  of  incidence  for  light 
polarised  in  and  at  right  angles  to  the  plane  of  incidence.  The 
absorptions  and  the  corresponding  photo-electric  currents  are  shown 
in  Fig.  62.  Curves  (1)  and  (2)  represent  the  photo-electric 
currents  due  to  light  polarised  at  right  angles  and  in  the  plane  of 
incidence  respectively,  curves  (3)  and  (4)  the  absorptions  of  the  light 
in  these  cases.  It  will  be  seen  that  in  each  case  the  current  and 
absorption  increase  and  decrease  together,  but  that  a  given  amount 
of  absorbed  light  is  very  much  more  efficacious  in  producing  dis- 
charge when  its  plane  of  polarisation  is  at  right  angles  to,  than 


236 


IONISATION   BY   LIGHT. 


[123 


when  it  is  in,  the  plane  of  incidence.  The  connection  between  the 
absorption  and  current  is  made  clearer  by  the  following  considera- 
tions given  by  Elster  and  Geitel.  Suppose  the  intensity  of  the 
incident  light  polarised  at  right  angles  to  the  plane  of  incidence 
is  unity,  let  the  amount  of  light  absorbed  when  the  angle  of 
incidence  is  </>  be  a$,  and  a0  when  <f>  =  0,  then  when  the  angle  of 
incidence  is  <£,  the  component  of  the  electric  force  parallel  to  the 


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**^ 

2 

^ 

3 

10° 

20° 

30° 

40° 

Fig. 

5 
62. 

_o 

60°    7 

_o 

80°    9( 

surface  is  proportional  to  cos  <£,  and  the  energy  corresponding  to 
this  component  to  cos2  </> ;  the  amount  of  this  energy  absorbed  will 
be  a0  cos3  <f>,  hence  a^  —  a0  cos8  </>  will  be  the  energy  due  to  the 
electric  force  at  right  angles  to  the  surface  absorbed  by  the  metal. 
Suppose  /^  is  the  current  when  the  angle  of  incidence  is  <f>,  I9  the 
current  when  the  angle  of  incidence  is  zero  for  unit  intensity  of 
light,  the  intensity  due  to  the  electric  force  parallel  to  the  surface 
is  cos2  <£,  the  current  due  to  this  is  J0  cos3  <f>,  hence  the  current 
arising  from  the  component  of  the  electric  force  perpendicular  to 
the  surface  may  be  taken  to  be  /^  —  /0  cos3  <£.  Now  Elster  and 
Geitel  have  shown  that  a^  —  a0  cos2  <£  and  /^  —  70  cos*  $  are  approxi- 
mately proportional  to  each  other ;  this  is  shown  by  the  two  curves 
in  Fig.  63,  which  represent  the  variation  of  the  two  quantities 
with  the  angle  of  incidence.  The  continuous  line  represents  the 
variation  of  the  current,  the  dotted  line  that  of  the  absorption. 


123] 


PHOTO-ELECTRIC   EFFECTS. 


237 


If  we  take  the  view  that  the  photo-electric  effect  is  due  to 
the  emission  of  negatively  electrified  corpuscles  from  the  metal, 
we  can  explain  the  influence  of  the  orientation  of  the  planes  of 
polarisation  as  follows.  We  may  suppose  that  the  energy  from 
the  light  absorbed  by  the  metal  goes  into  some  of  the  corpuscles, 
giving  them  sufficient  kinetic  energy  to  escape  from  the  metal, 
just  as  they  are  able  to  do  at  a  very  high  temperature.  These 
corpuscles  have  acquired  from  the  ultra-violet  light  very  much 


40 


24 


12 


10 


20 


30 


40 


50 


60 


70 


80 


80 


Angle  of  incidence. 
Fig.  63. 

more  kinetic  energy  than  is  possessed  by  a  molecule  of  a  gas  at  the 
temperature  of  the  metal ;  thus  every  collision  a  corpuscle  makes 
with  the  molecules  of  the  metal  will  result  in  a  loss  of  kinetic 
energy,  so  that  if  it  is  to  escape  from  the  metal  it  is  important  that 
it  should  make  as  few  collisions  as  possible  before  reaching  the 
surface,  i.e.  that  it  should  move  approximately  at  right  angles  to 
the  surface.  When  the  light  is  polarised  at  right  angles  to  the 
plane  of  incidence  there  is  a  component  of  the  electric  force  at 
right  angles  to  the  surface  which  will  direct  some  of  the  corpuscles 
in  this  direction,  when  however  the  light  is  polarised  in  the  plane 
of  incidence  the  electric  force  is  parallel  to  the  surface  and  tends 
to  make  the  corpuscles  move  parallel  to  the  surface  instead  of 
towards  it ;  thus  the  corpuscles  have  in  order  to  escape  to  make 
more  collisions  in  this  case  than  the  former,  and  so  are  less  likely 
to  reach  the  surface  with  sufficient  energy  to  escape  from  it. 


238  IONISATION  BY   LIGHT.  [124 


Influence  of  Temperature  on  the  Photo-electric  Effect. 

124.  The  influence  of  the  temperature  of  the  metal  on  the 
photo-electric  effect  has  been  investigated  by  Hoor*,  Stoletow  f, 
Elster  and  Geitel  J,  Righi§,  and  Zeleny||.  Hoor  found  that  the 
sensitiveness  of  a  zinc  plate  to  light  diminished  when  the  tem- 
perature was  raised  from  18°  to  55°.  Stoletow  found  on  the  other 
hand  that  raising  the  temperature  to  200°  C.  increased  the  sensi- 
tiveness, Elster  and  Geitel  that  an  alteration  of  temperature  had 
no  effect  on  zinc.  Righi  found  that  the  positive  charge  given  by 
light  to  a  previously  uncharged  plate  was  greater  when  the  plate 
was  hot  than  when  it  was  cold :  we  must  remember  that  a  blast 
of  air  blowing  across  the  plate  increases  the  positive  charge  so 
that  part  of  the  effect  observed  by  Righi  may  have  been  due  to  air 
currents  set  up  by  the  hot  plate.  In  considering  the  interpre- 
tation of  these  seemingly  discrepant  results  we  must  remember 
that  the  circumstances  which  affect  the  sensitiveness  of  the  metal 
to  the  light  will  depend  very  much  upon  the  strength  of  the  field. 
Thus  supposing  we  are  dealing  with  a  strong  field  and  the  gas 
surrounding  the  metal  is  at  an  exceedingly  low  pressure,  the 
photo-electric  current  is  saturated  and  measures  the  number  of 
corpuscles  given  off  from  the  metal  in  unit  time ;  measurements  of 
the  effect  of  temperature  in  this  case  would  admit  of  a  perfectly 
definite  interpretation,  but  when  the  gas  is  at  a  high  pressure  and 
the  strength  of  the  field  is  weak,  i.e.  when  we  are  working  on  the 
earlier  part  of  the  curve  connecting  the  current  and  the  electro- 
motive force,  then  the  interpretation  of  the  effect  of  temperature 
is  ambiguous,  for  the  current  at  this  stage  depends  not  only  upon 
the  rate  of  emission  of  the  corpuscles,  but  also  upon  the  velocity  of 
the  ions  through  the  gas.  Now  the  increase  in  temperature  may 
alter  the  density  of  the  gas,  and  hence  the  velocity  of  the  ions 
through  it,  and  it  would  require  further  experiments  to  disentangle 
this  effect  of  the  velocity  of  the  ions  from  the  effect  on  the  rate 
of  emission  of  the  corpuscles  from  the  plate.  The  experiments 

*  Hoor,  Wien.  Berichte,  xcvii.  p.  719,  1888.     Exner's  Rep.  xxv.  p.  91,  1889. 

t  Stoletow,  Comptes  Rendus,  cviii.  p.  1241,  1889. 

t  Elster  and  Geitel,  Wied.  Ann.  xlviii.  p.  625,  1893. 

§  Righi,  Atti  1st.  Yen.  vii.  Mem.  11. 

il   Zeleny,  Physical  Review,  xii.  p.  321,  1901. 


124] 


PHOTO-ELECTRIC   EFFECTS. 


239 


of  Elster  and  Geitel  on  the  effect  of  temperature  on  the  current 
from  a  potassium  surface  in  a  good  vacuum  are  not  open  to  this 
objection,  as  the  effect  of  the  gas  is  eliminated,  and  in  this  case 
they  found  an  increase  in  the  current  of  about  50  per  cent,  when 
the  temperature  was  increased  from  20°  to  50°:  from  some  experi- 
ments made  by  the  writer  it  appears  that  when  the  temperature 
is  raised  considerably  higher,  say  to  200°,  there  is  a  very  great 
increase  in  the  current  from  the  alkali  metals,  and  that  these  are 
very  much  more  sensitive  to  light  at  high  temperatures  than  they 
are  at  low. 

Zeleny,  who  measured  the  current  from  platinum  and  iron 
exposed  to  ultra-violet  light  and  surrounded  by  air  at  atmospheric 


Electrometer  Deflection. 

•*  10  (0 
80  o 

0  0 

, 

1 

/ 

/ 

/ 

/ 

/ 

/ 

1 

/ 

' 

\ 

^ 

7 

S 

\ 

/ 

' 

^ 

^^ 

100          200           300          400          500          8OO          7C 
Temperature. 
Fig.  64. 

pressure,  found  that  from  platinum  the  current  first  decreased 
as  the  temperature  increased,  reached  a  minimum,  and  then 
increased  with  the  temperature  as  far  as  the  highest  temperature 
used.  The  results  showed  a  curious  hysteresis  effect  in  the  currents 
obtained,  when  the  metal  was  cooling  they  were  greater  than  those 
at  the  same  temperature  when  the  wire  was  getting  hotter.  These 


240 


IONISATION   BY   LIGHT. 


[124 


results  are  indicated  in  the  curves  shown  in  Fig.  65,  where  (i) 
represents  the  currents  corresponding  to  continuously  increasing 
temperatures,  (ii)  those  for  continuously  decreasing  temperatures ; 
(iii)  those  for  increasing  temperatures,  and  (iv)  for  decreasing 
temperatures  when  the  wire  was  cooled  to  the  temperature  of  the 
room  between  each  observation.  These  observations  show  that 
heating  the  wire  produces  some  change  in  the  surface,  possibly  in 
the  amount  of  gas  condensed  upon  it  or  absorbed  by  the  metal, 
from  which  it  only  slowly  recovers.  With  iron  the  minimum 
current  is  not  nearly  so  clearly  marked  as  with  platinum,  nor  is 
there  so  great  a  difference  between  the  curves  for  increasing  as 


300 


200 


H   iOO 


^ 


\ 


500' 


600°        700* 


0  100*         200'          300*        400' 

Temperature. 
Fig.  65. 

those  for  decreasing  temperature ;  on  the  other  hand  the  photo- 
electric current  increases  more  rapidly  with  the  temperature  for 
iron  than  for  platinum,  the  current  at  700°  C.  being  for  iron  about 
40  times  the  current  at  15°  C.,  while  for  platinum  the  current  at 
700°  C.  was  only  about  2'5  times  that  at  15°  C. 

^eleny  also  investigated  whether,  if  the  metal  were  raised  to 
a  temperature  just  below  that  at  which  it  would  begin  to  give  off 
positive  ions  in  the  dark,  it  could  be  made  to  give  off  positive  ions 
by  the  incidence  upon  it  of  ultra-violet  light;  the  positive  ions 


125]  PHOTO-ELECTRIC   EFFECTS.  241 

were  however  not  produced  at  a  lower  temperature  in  the  light 
than  in  the  dark.  Nor  when  the  metal  was  raised  to  the  tem- 
perature at  which  the  positive  ions  were  produced  was  the  rate 
of  production  increased  by  the  incidence  of  ultra-violet  light. 

The  experiments  of  Elster  and  Geitel  and  Zeleny  seem  to 
establish  the  fact  that  the  photo-electric  effects  of  metals  are 
greater  at  a  high  temperature  than  at  a  low  one.  This  is  what  we 
should  expect  if  we  take  the  view  that  the  photo-electric  effect 
is  due  to  the  acquisition  by  the  corpuscles  in  the  metal  under  the 
action  of  the  ultra-violet  light  of  sufficient  kinetic  energy  to  enable 
them  to  escape  from  the  metal.  The  higher  the  temperature  the 
greater  would  be  the  initial  kinetic  energy  possessed  by  the 
corpuscles,  and  the  smaller  the  increment  required  to  enable  them 
to  move  fast  enough  to  escape  from  the  metal. 


Nature   of  the  ions  produced   by  the  action  of  ultra-violet  light 

on  metals. 

125.  The  experiments  made  by  the  author  and  Lenard  (see 
p.  107)  show  that  in  high  vacua  metals  when  illuminated  with 
ultra-violet  light  give  out  corpuscles,  i.e.  bodies  whose  mass  is 
only  about  y^-  of  that  of  the  hydrogen  atom;  when  however 
the  metal  is  surrounded  by  gas  the  corpuscles  soon  strike  against 
the  molecules,  get  attached  to  them  and  have  to  drag  them 
along  with  them  as  they  move  under  the  action  of  the  electric 
field.  The  velocity  of  the  negative  ions  through  different  gases 
has  been  measured  by  Rutherford  (see  p.  52),  who  showed  that 
the  velocity  of  the  ion  did  not  depend  upon  the  nature  of  the 
metal  on  which  the  light  fell,  but  that  it  did  depend  on  the  nature 
of  the  gas  through  which  the  ion  had  to  travel,  and  that  the 
velocity  through  any  gas  of  the  negative  ion  produced  by  ultra- 
violet light  was  very  approximately  the  same  as  that  of  the  ion 
produced  by  Rontgen  rays  through  the  same  gas. 

The  diminution  of  the  photo-electric  effect  produced  when  the 
pressure  of  the  gas  is  low  by  a  transverse  magnetic  field,  which 
was  discovered  by  Elster  and  Geitel*,  has  already  been  discussed 
on  page  107. 


Elster  and  Geitel,  Wied.  Ann.  xli.  p.  166,  1890. 


T.  G.  16 


242  IONISATION  BY   LIGHT.  [126 

The  photo-electric  effect  does  not  persist  after  the  light  is  cut 
off.  Stoletow*,  who  made  a  series  of  experiments  on  this  point, 
'could  not  obtain  any  evidence  that  there  was  any  finite  interval 
between  the  incidence  of  the  light  and  the  attainment  of  the  full 
photo-electric  effect,  or  between  the  eclipse  of  the  light  and  the 
total  cessation  of  the  effect,  and  he  showed  that  the  interval  must 
at  any  rate  be  less  than  y^  of  a  second. 

126.  Connection  betiueen  photo-electric  effects  and  the  fluorescence 
and  ionisation  of  solutions.  G.  C.  Schmidt  f  made  a  series  of 
experiments  on  this  subject,  with  the  result  that  there  was  no 
clear  evidence  of  any  intimate  relation  between  photo-electric 
effects,  ionisation  and  fluorescence :  for  while  in  fuchsme  there 
seemed  to  be  clear  indications  of  a  connection  between  ionisation 
and  photo-electric  effects — since  aqueous  solutions  of  fuchsine 
are  photo-electric,  while  solutions  in  alcohol  and  acetone  are  not, 
and  fuchsine  is  ionised  in  water  and  not  in  the  other  solvents — the 
results  with  eosine  seemed  decisive  against  this  connection,  as 
the  addition  of  neutral  salts,  such  as  potassium  iodide  or  sodium 
chloride,  destroys  the  ionisation,  while  in  aqueous  solutions  it  has 
no  influence  upon  the  photo-electric  effects.  Again,  magdala 
red  fluoresces  in  alcohol,  amyl-alcohol  and  acetone,  the  first  two 
solutions  are  photo-electric,  the  last  is  not.  Salts  which  undergo 
decomposition  in  the  light  such  as  the  haloid  salts  of  silver  are 
strongly  photo-electric. 

In  the  case  of  water  a  change  in  the  physical  state  seems  to 
be  accompanied  by  a  change  in  the  photo-electric  properties,  as 
dry  ice  was  found  by  BrillouinJ  to  be  photo-electric,  while  water 
in  the  liquid  state  is  not. 

The  opinion  has  been  advanced  by  Cantor§  and  Knoblauch ||, 
that  the  photo-electric  effect  depends  upon  oxidation,  on  the 
ground  that  the  substances,  elementary  and  compound,  which 
exhibit  this  effect  are  those  which  combine  with  oxygen;  it  is 
however,  I  think,  necessary  to  distinguish  between  the  poiver  of 

*  Stoletow,  Aktinoelektrische   Untersuchungen,  Physikalisch.  Revue,   i.   p.  725, 
1892. 

f  G.  C.  Schmidt,  Wied.  Ann.  Ixiv.  p.  708,  1898. 

J  Brillouin,  Eel.  Electr.  xiii.  p.  577,  1897. 

§  Cantor,  Wien.  Sitzungsber.  102,  p.  1188,  1893. 

||  Knoblauch,  Ze.it.  f.  Physikalische  Chemie,  xxix.  p.  527,  1899. 


126]  PHOTO-ELECTRIC   EFFECTS.  243 

combining  with  oxygen  and  the  act  of  combination.  We  should 
expect  the  photo-electric  substances  to  be  oxidisable,  as  they  lose 
readily  negative  corpuscles,  and  thus  get  positively  charged  and 
in  a  fit  state  to  combine  with  an  electro-negative  substance  like 
oxygen ;  there  is  no  evidence  however  that  the  presence  of  oxygen 
is  necessary  for  the  photo-electric  effect,  in  fact  the  evidence  the 
other  way  seems  quite  conclusive,  for  substances  like  rubidium 
and  potassium  enclosed  in  highly  exhausted  vessels  seem  to 
retain  their  photo-electric  power  indefinitely,  and  any  trace  of 
oxygen  originally  present  would  soon  be  absorbed  by  the  metals. 


16—2 


CHAPTER  XI. 

IONISATION   BY  RONTGEN   RAYS. 

127.  WE  shall  in  this  chapter  mainly  confine  our  attention  to 
the  ionising  properties  of  the  rays,  leaving  for  future  consideration 
the  manner  of  their  production  and  a  discussion  of  their  nature ; 
it  will  however  be  convenient  to  enumerate  some  of  their  most 
important  properties.  Rontgen*  found  in  1895  that  very  remark- 
able effects  occurred  in  the  neighbourhood  of  a  highly  exhausted 
tube  through  which  an  electric  discharge  was  passing ;  the  exhaus- 
tion of  the  tube  being  so  great  that  a  vivid  green  phosphorescence 
appeared  on  the  glass.  He  found  that  a  plate  covered  with  a  phos- 
phorescent substance  such  as  potassium-platino-cyanide  became 
luminous  when  placed  near  the  tube,  and  that  a  thick  plate  of 
metal  cast  a  sharp  shadow  when  placed  between  the  tube  and  the 
plate ;  while  light  substances,  such  as  thin  aluminium,  cardboard, 
wood,  cast  but  slight  shadows,  showing  that  the  agent  which 
produced  the  phosphorescence  on  the  plate  could  traverse  with 
considerable  freedom  bodies  which  are  opaque  to  ordinary  light. 
As  a  general  rule  the  greater  the  density  of  a  substance  the  more 
opaque  it  is  to  this  agent ;  thus  the  bones  are  much  more  opaque 
to  this  effect  than  the  flesh,  so  that  if  the  hand  is  placed  between 
the  discharge  tube  and  the  plate  the  outlines  of  the  bones  are 
distinctly  visible  in  the  shadow  cast  on  the  screen,  or  if  a  purse  con- 
taining coins  is  placed  between  the  tube  and  the  plate  the  purse 
itself  casts  but  little  shadow,  while  the  coins  cast  a  very  dense 
one.  Rontgen  showed  that  the  agent,  now  called  Rontgen  rays, 
producing  the  phosphorescence  on  the  plate  is  propagated  in 
straight  lines,  and  is  not  bent  in  passing  from  one  medium  to 

*  Bontgen,  Wied.  Ann.  Ixiv.  p.  1,  1898  (reprinted  from  the  original  paper  in  the 
Sitzungsberichte  der  Witrzburger.  Physik.  Med.  Gesellsch.  1895). 


127]  IONISATION   BY   RONTGEN   RAYS.  245 

another ;  there  is  thus  no  refraction  of  the  rays.  The  rays  affect  a 
photographic  plate  as  well  as  a  phosphorescent  screen  and  shadow 
photographs  can  readily  be  taken :  the  time  of  exposure  depends 
on  the  intensity  of  the  rays,  and  this  depends  on  the  discharge 
through  the  tube  and  on  the  substances  traversed  by  the  rays  in 
their  passage  to  the  plate ;  the  time  of  exposure  required  to 
produce  a  photograph  may  vary  from  a  few  seconds  to  several 
hours.  The  power  of  the  rays  to  penetrate  obstacles  in  their  path 
varies  very  much  with  the  condition  of  the  discharge  tube  from 
which  they  originate ;  when  the  pressure  in  this  tube  is  not  very 
low,  and  the  potential  difference  between  its  electrodes  conse- 
quently comparatively  small,  the  rays  have  but  little  penetrating 
power  and  are  readily  absorbed ;  such  rays  are  called  '  soft  rays.' 
If  the  exhaustion  of  the  tube  is  carried  much  further,  so  that  the 
potential  difference  between  the  electrodes  is  greatly  increased, 
the  Rontgen  rays  have  much  greater  penetrating  power  and  are 
called  'hard  rays.'  With  a  very  highly  exhausted  bulb  and  a 
large  induction  coil  it  is  possible  to  get  rays  which  will  produce 
appreciable  effects  after  passing  through  sheets  of  brass  or  iron 
several  millimetres  thick.  The  difference  in  penetrating  power  is 
well  shown  by  observing  the  changes  which  take  place  in  the 
shadow  of  a  hand  on  a  phosphorescent  screen,  as  the  pressure  of 
the  gas  in  the  discharge  tube  is  gradually  reduced.  When  first 
the  rays  appear  they  are  so  'soft'  that  they  are  stopped  by  the 
flesh  as  well  as  the  bones,  so  that  the  bones  are  very  indistinctly 
seen ;  when  the  exhaustion  proceeds  further  the  rays  get  harder, 
and  are  able  to  penetrate  the  flesh  but  not  the  bones.  At  this 
stage  the  difference  between  the  shadow  of  the  flesh  and  the 
bones  is  most  distinct ;  when  the  exhaustion  proceeds  further  the 
rays  get  so  hard  that  they  are  able  to  penetrate  the  bones  as  well 
as  the  flesh  and  the  shadow  again  becomes  indistinct.  Not  only 
may  the  rays  from  different  discharge  tubes  be  different,  but  even 
the  same  bulb  may  emit  at  the  same  time  rays  of  different  degrees 
of  hardness.  The  property  by  which  it  is  most  convenient  to 
identify  a  ray  is  its  hardness,  and  this  is  conveniently  measured 
by  the  amount  of  absorption  when  it  passes  through  a  layer  of 
aluminium  or  tinfoil  of  given  thickness.  Now  in  some  experi- 
ments made  by  the  writer  and  McClelland*  on  the  absorption 

*  J.  J.  Thomson  and  McClelland,  Proc.  Camb.  Phil.  Soc.  ix.  p.  126,  1899. 


246  IONISATION  BY   RONTGEN    RAYS.  [128 

produced  when  the  rays  passed  through  one  layer  of  tinfoil  after 
another,  it  was  found  that  the  absorption  produced  by  the  first  few 
sheets  of  tinfoil  traversed  by  the  rays  was  much  greater  than 
that  due  to  the  same  number  of  sheets  after  the  rays  had  already 
travelled  through  several  sheets  of  tinfoil.  This  shows  that  some 
of  the  ray^  are  readily  absorbed  by  the  tinfoil  while  others  pass 
through  with  much  greater  facility,  thus  the  first  few  layers  of 
tinfoil  would  stop  the  first  kind  of  rays  while  the  remainder  pass 
through  with  comparatively  little  absorption.  McClelland  showed 
that  if  he  took  plates  of  different  metals,  the  thickness  of  the 
plates  being  chosen  so  that  they  gave  the  same  absorption  for  the 
rays  from  one  tube,  they  would  not  necessarily  give  the  same 
absorption  for  the  rays  from  another. 

The  Rontgen  rays  when  they  pass  through  a  gas  make  it  a 
conductor  of  electricity,  they  ionise  the  gas*:  the  number  of  ions 
produced  in  one  second  in  one  cubic  centimetre  of  the  gas  by  rays 
of  given  intensity  depends  upon  the  pressure  of  the  gas,  the 
nature  of  the  gas  and  its  temperature. 

128.  Effect  of  Pressure.  Perrinf  has  shown  that  the  rate  of 
production  of  ions  per  cubic  centimetre  by  rays  of  given  intensity 
is  proportional  to  the  pressure  of  the  gas.  He  proved  this  by 
showing  that  the  saturation  current  through  a  given  volume  of 
gas  was  proportional  to  the  pressure  :  the  current  passed  between 
two  large  plates  of  metal,  care  being  taken  that  the  rays  did  not 
fall  upon  the  plates ;  this  precaution  is  necessary,  because  as  we 
shall  see  when  the  Rontgen  rays  fall  upon  metal  secondary  rays 
are  produced  which  ionise  the  gas,  and  complicate  the  effects ;  in 
addition  to  this  precaution  it  is  necessary  to  arrange  the  electric 
field  so  that  all  the  gas  exposed  to  the  rays — or  at  least  all  of  it 
from  which  the  ions  can  move  to  the  electrodes — is  under  the 
influence  of  an  electric  field  strong  enough  to  produce  saturation, 
for  unless  saturation  is  reached  throughout  the  whole  of  the  gas 
the  current  will  depend  upon  the  velocity  of  the  ions  under  the 
electric  field  as  well  as  upon  the  number  of  ions  produced ;  as  the 
velocity  of  the  ions  increases  as  the  pressure  diminishes  the 
unsaturated  current  will  diminish  less  rapidly  with  the  density 

*  J.  J.  Thomson,  Camb.  Univ.  Reporter,  Feb.  4,  1896.    Benoist  and  Harmozescu, 
C.  R.  cxxii.  p.  235,  1896.     Righi,  Ace.  del  Lincei  (5),  v.  p.  143,  1896. 
t  Perrin,  Annales  de  Chimie  et  de  Physique  [7],  xi.  p.  496,  1897.  . 


129] 


IONISAT1ON   BY   RONTGEN   RAYS. 


247 


than  the  saturated  one.  In  fact  when  the  electric  field  is  feeble 
the  current  will  increase  as  the  pressure  diminishes,  for  if  n  is 
the  number  of  positive  or  negative  ions  per  cubic  centimetre,  q 
the  number  of  ions  produced  in  one  second  in  a  cubic  centimetre, 
then  (see  p.  15)  n  —  (#/«)*;  the  current  under  a  small  electric 
force  X  is  equal  to  ne X  (u  -4-  v\  where  e  is  the  charge  en  an  ion, 
u  and  v  the  velocities  of  the  positive  and  negative  ions  under  unit 
electric  field.  Now  n  is  proportional  to  V^,  and  therefore  to  Vp 
p  being  the  pressure  of  the  gas,  since  (see  p.  19)  a  is  independent 
of  p,  while  u  and  v  are  proportional  to  l/p ;  the  current  under 
small  electric  forces  will  vary  as  1/Vp. 

129.  lonisation  of  Different  Gases.  When  Rontgen  rays  of  the 
same  intensity  pass  through  different  gases  at  the  same  pressure 
the  amount  of  ionisation  depends  greatly  upon  the  composition  of 
the  gas;  the  number  of  ions  produced,  measured  by  the  satura- 
tion current,  is  least  in  hydrogen,  and  for  the  gases  hitherto  tried 
greatest  in  the  vapour  of  methyl  iodide :  it  is  also  exceedingly 
large  for  mercury  vapour:  the  relative  values  of  q — the  number 
of  ions  produced  in  one  second  in  a  cubic  centimetre  of  the  gas  at 
atmospheric  pressure  and  temperature — are  given  in  the  following 
table.  The  number  for  air  is  taken  as  unity. 


1 

2 

Gas 

Perrin  * 

Ruther- 
ford t 

Thom- 
son J 

Gas 

Perrin 

Ruther- 
ford 

Thom- 
son 

H2 

•026 

•5 

•33 

C2N2 

1-05 

N2 

.  .. 

•9 

•89 

C2H2 

•  •• 

... 

1 

02 
C02 
CO" 

1-34 

12 
1  2 

1-1 
1-4 

•86 

HC21 

6* 

8 

6 
4 
11 

6 
6-4 

8-9 

NO 
N20 

1-3 

1-08 
1-4?- 

CL 
NH3 

"•1  ? 

18 

17'4 
1? 

We  see  that  though  the  results  of  different  observers  are  in 
fair  agreement  for  most  gases,  for  hydrogen  they  are  very  dis- 
cordant. We  must  remember  that  different  observers  used  rays 
of  different  degrees  of  hardness,  and  that  it  is  probable  that  the 

*  Perrin,  Annales  de  Physique  et  de  Chimie  [7],  xi.  p.  496,  1897. 

t  Rutherford,  Phil.  Mag.  v.  43,  p.  241,  1897. 

J  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  x.  p.  10,  1900. 


248 


IONISATION   BY   KONTGEN   RAYS. 


[130 


relative  ionisation  in  two  gases  depends  upon  the  kind  of  rays  used 
to  ionise  them.  The  gases  in  which  the  ionisation  is  large  have 
also  large  refractive  indices,  it  does  not  however  seem  that  a  large 
refractive  index  necessarily  implies  large  ionisation  ;  for  example, 
the  refractive  index  of  acetylene  C2H2  as  determined  by  Mascart 
is  very  nearly  the  same  as  that  of  sulphuretted  hydrogen  H2S,  yet 
the  ionisation  in  the  H2S  is  about  six  times  that  in  C2H2.  The 
ionisation  by  the  Rontgen  rays  does  not  seem  to  be  closely 
connected  with  the  density  of  the  gas  ;  thus  the  density  of  H2S  is 
a  little  greater  than  that  of  O2  and  considerably  less  than  that  of 
C02,  yet  the  ionisation  in  either  of  these  gases  is  small  compared 
with  that  in  H2S.  In  other  cases  of  ionisation  such  as  that  due 
to  radiation  from  some  radio-active  substances,  or  to  the  passage  of 
cathode  rays  through  a  gas,  we  shall  see  that  the  ionisation  is  much 
more  closely  connected  with  the  density  of  the  gas,  being  (except 
in  the  case  of  hydrogen)  directly  proportional  to  the  density. 

130.  The  writer*  pointed  out  that  the  measurements  given 
in  the  above  table  indicate  that  the  ionisation  of  a  gas  is  approxi- 
mately an  additive  property,  i.e.  if  2  [A]  is  the  value  of  q  for  a  gas 
A2,  2  [B]  the  value  for  a  gas  B2  and  so  on,  then  the  value  of  q  for 
a  gas  AiBmCn  will  be  I  [A]  +  m  [B]  +  n  [C].  Thus  if  we  use  the 
numbers  given  in  the  third  column  of  the  preceding  table  for 
H2,  N2,  O2,  C02,  SO2,  and  C12  to  determine  the  values  of  2[H], 
2  [N],  etc.,  we  find 

=  165,          [C]=    '3, 


-55, 

if  we  use  these  numbers  to  calculate  the  ionisation  in  the  other 
gases  in  the  table  using  the  additive  rule  we  get  the  following 
results. 


Gas 

Ionisation 
observed 

Ionisation 
calculated 

Gas 

Ionisation 
observed 

Ionisation 
calculated 

CO 

•86 

•85 

Og-H^ 

1 

•93 

NO 
Ni° 

1-08 
1-47 

•995 
1-44 

HC1 

6 
8-9 

5-63 

8-86 

Cjft 

1-05 

1-49 

NH3 

1 

•94 

*  Loc.  cit. 


130]  IONISATION   BY   RONTGEN   RAYS.  249 

Thus  except  in  the  case  of  C2N2  the  agreement  is  within  the 
limits  of  the  errors  of  experiment. 

Connection  between  the  absorption  of  the  rays  by  a  gas  and  the 
ionisation  produced  in  a  gas  by  the  rays.  The  rays  are  absorbed 
by  gases  through  which  they  pass,  the  amount  of  this  absorption 
has  been  measured  by  Rutherford*,  who  used  for  this  purpose  the 
apparatus  represented  in  Fig.  66.  Two  large  and  similar  conical 


Fig.  66. 

vessels  ABC,  A'B'C',  much  larger  at  the  top  than  at  the  bottom, 
were  placed  in  such  positions  that  the  axis  of  each  cone  passed  as 
nearly  as  possible  through  the  anode  of  the  tube  producing  the 
Rontgen  rays.  The  upper  parts  of  the  vessels  AB,  A'B'  were 
made  of  lead,  and  were  separated  from  the  lower  portions,  which 
were  made  of  glass,  by  thin  plates  of  ebonite,  similar  plates 
covered  the  ends  of  the  glass  cylinders  at  C  and  C',  so  that  the 
vessels  BC,  B'C'  were  air-tight  and  could  be  exhausted  when 
required.  The  intensities  of  the  rays  after  they  had  passed 
through  the  glass  cylinders  were  measured  by  determining  the 
saturation  currents  through  the  lead  cylinders  AB,  A'B'.  In- 
sulated wires  DE,  D'E'  were  used  as  the  electrodes,  these  were 
connected  with  opposite  pairs  of  quadrants  of  an  electrometer, 
both  initially  charged  to  the  same  potential.  The  outsides  of 
the  vessels  AB,  A'B'  were  connected  with  the  earth.  The  posi- 
tion of  the  bulb  giving  the  rays  was  adjusted  so  that  when  the 
glass  vessels  BC,  B'C'  were  filled  with  air  at  the  same  pressure 

*  Rutherford,  Phil.  Mag.  v.  43,  p.  241,  1897. 


250 


IONISATION   BY   RONTGEN    RAYS. 


[1:30 


the  needle  of  the  electrometer  remained  at  rest  when  the  rays 
were  passing  through  the  vessel  ;  this  showed  that  the  potentials 
of  each  pair  of  quadrants  were  falling  at  the  same  rate,  and 
therefore  that  the  currents  through  the  vessels  AS,  A'E'  were 
equal.  If  the  gas  were  removed  from  one  of  the  vessels  BC,  B'C' 
or  another  gas  introduced,  the  balance  was  disturbed,  thus 
showing  the  absorption  of  the  rays  by  the  gas  in  the  vessel. 
If  we  assume  that  the  energy  absorbed  when  the  rays  pass 
through  unit  length  of  the  gas  is  proportional  to  the  energy  of  the 
rays  /  and  equal  to  X/,  then  the  change  87  in  the  intensity  when 
the  rays  traversed  a  distance  Bx  is  given  by  the  equation 


or 


a/  =- 


r_  T  P-\x 

J.  —  J.Q  6         , 


where  /0  is  the  intensity  of  the  rays  when  x  =  0.  Thus  if  /  is  the 
length  of  path  of  the  rays  through  the  vessel  BC,  the  ratio  of  the 
intensity  of  the  radiation  in  AB  when  BC  is  full  of  a  gas  whose 
coefficient  of  absorption  is  X,  to  the  intensity  when  BC  is  exhausted 
is  equal  to  e~ZA,  in  this  way  X  can  be  determined.  Rutherford  found 
that  for  air  X  is  about  10~3,  so  that  the  rays  lose  about  1  per  cent, 
of  their  energy  in  passing  through  10  cm.  of  air  at  atmospheric 
pressure  ;  about  7  cm.  of  mercury  vapour  at  atmospheric  pressure 
and  at  the  temperature  of  boiling  mercury  reduced  the  intensity 
of  the  rays  to  about  £.  The  values  of  X  for  different  gases  are 
given  in  the  following  table.  The  third  column  of  this  table 
contains  the  relative  values  of  q — the  number  of  ions  produced  in 
each  volume  in  unit  time  by  rays  of  equal  intensity. 


Gas 

X 

q 

Gas 

X 

q 

Hydrogen  
Air  .  . 

small 
•001 

about 
•001 

•5 
1 
1-2 
•9 
•8 
1-2 

Sulphur  dioxide  

•0025 
•0037 
•0065 
•0095 
•1 
•07 

4 
6 
11 

18 

Sulphuretted  hydrogen 
Hydrochloric  acid  
Chlorine    

Oxygen  } 
Nitrogen  1 
Coal  gas  j 

Carbon  dioxideJ 

Methyl  iodide  

These  numbers  show  that  good  conductors  under  the  rays  are 
good  absorbers  of  the  radiation :  if  the  conductivity  were  pro- 
portional to  the  radiation,  i.e.  if  q/\  were  constajtfe,  then  if  the 


131]  IONISATION   BY   RONTGEN   RAYS.  251 

whole  of  the  radiation  were  absorbed  by  a  gas  the  number  of  ions 
produced  would  be  independent  of  the  nature  of  the  gas.  For 
if  70  is  the  initial  intensity  of  the  rays  the  intensity  after  they 
have  passed  through  a  distance  x  of  the  gas  is  I^-**,  hence  the 
number  of  ions  produced  in  unit  time  in  the  space  dx  is  pro- 
portional to  qI06~^c,  thus  the  total  number  of  ions  produced  in  the 
gas  in  unit  time  is  proportional  to 


and  this  is  equal  to  qlj\  :  thus  if  q/\  is  the  same  for  all  gases  the 
total  number  of  ions  produced  by  rays  of  given  intensity  will  be 
the  same.  The  numbers  given  above  for  q/\  show  considerable 
variations  in  the  different  gases  :  the  discrepancies  however  chiefly 
occur  in  the  gases  for  which  X  is  very  small,  and  in  which  the 
errors  of  experiment  are  necessarily  large. 

Rutherford  and  M°Clung*  have  recently  made  very  careful 
determinations  of  the  values  of  X  for  carbonic  acid  and  air;  they 
found  the  ratio  for  the  two  gases  was  1*59,  for  the  ratio  of  the 
currents  they  found  T43,  but  they  consider  the  current  through 
the  carbonic  acid  was  not  quite  saturated.  I  found  the  ratio  of 
the  currents  through  the  two  gases  to  be  1*53,  which  is  very  nearly 
the  ratio  of  the  absorption.  The  value  of  X  depends  upon  the 
character  of  the  rays,  for  hard  rays  it  is  very  much  smaller  than 
for  soft  ones,  thus  the  value  of  X  for  air  in  Rutherford  and 
Ml'Clung's  experiments  was  only  about  one-quarter  of  the  value 
in  Rutherford's  earlier  experiments  in  which  softer  rays  were  used. 
In  the  case  of  the  radiation  from  uranium  —  which  is  much  more 
easily  absorbed  than  Rontgen  rays  —  Rutherford  f  has  shown  that 
when  all  the  radiation  is  absorbed  by  a  gas,  the  total  amount  of 
ionisation  is  approximately  the  same  in  all  gases. 

The  absorption  depends  upon  the  pressure  of  the  gas  :  usii,g 
the  vapour  of  methyl-iodide,  Rutherford  has  shown  that  down  to 
a  pressure  of  a  quarter  of  an  atmosphere  the  absorption  is  pro- 
portional to  the  pressure. 

131.  BenoistJ  concludes  from  experiments  on  the  vapours  of 
bromine  and  iodine,  of  ethyl-bromide  and  methyl-iodide  that  the 

*  Rutherford  and  McClung,  Phil.  Tram.  A,  cxcvi.  p.  25,  1901. 

t  Rutherford,  Phil.  Mag.  v.  47,  p.  109,  1899. 

t  Benoist,  Journal  de  Physique  [3],  x.  p.  653,  1901. 


252  IONISATION   BY   RONTGEN   RAYS.  [131 

absorption  produced  by  a  given  mass  of  a  substance  is  indepen- 
dent of  its  physical  state;  that,  for  example,  the  vapour  of  a 
volatile  liquid  or  solid  absorbs  the  same  amount  of  radiation  when 
in  the  gaseous  state  as  when  condensed  into  a  solid  or  liquid. 

Benoist  introduces  a  quantity  which  he  calls  the  coefficient  of 
transparency  of  the  substance  ;  it  is  the  weight  in  milligrammes 
of  a  prism  of  the  substance  on  a  base  one  square  centimetre 
in  area  which  produces  the  same  absorption  as  a  standard  prism 
of  paraffin-  wax  75  mm.  long,  when  the  rays  travel  along  the 
axes  of  the  prisms.  He  has  proved  the  very  important  law,  that 
if  we  have  a  mass  M  of  a  substance  whose  transparency  is  E  made 
up  of  masses  Mlt  M2,  M3...,  of  substances  whose  coefficients  of 
transparency  are  E1}  E2,  Es...,  then  whether  the  substances  are 
mechanically  mixed  or  in  a  state  of  chemical  combination 

M_M     M  •     M 

E~E,+E,+E^ 

I  think  the  meaning  of  this  law  is  made  clearer  by  the  intro- 
duction of  a  quantity  which  we  may  call  the  molecular  absorption 
of  the  substance,  i.e.  the  absorption  produced  by  one  molecule  of 
the  substance,  and  which  is  connected  with  the  Benoist  coefficient 
as  follows  :  suppose  that  the  mass  of  a  molecule  is  m,  and  that  in 
Benoist's  prisms  there  are  N  molecules,  then  Nm  =  c.E  where  c  is 
a  constant  ;  by  the  definition  of  E  these  N  molecules  produce  a 
given  amount  of  absorption  ;  hence  if  a  is  the  absorption  due  to 
one  molecule  Na  =  G  where  C  is  a  constant  ;  hence  we  see  that 

m 


where  X  does  not  depend  on  the  nature  of  the  substance.  Let  us 
now  express  Benoist's  law  in  terms  of  the  absorption  a.  If  there 
are  N!  molecules  of  the  first  substance,  JV2  of  the  second,  and  so  on 

2  =  N2mZ)   M=Nm, 


and  -TT  =  N\a  ; 

& 

thus  equation  (1)  becomes 

Na  =  Nlal  +  N2a2 

This  is  equivalent  to  the  statement  that  the  absorption  of  any 
substance  is  equal  to  the  sum  of  the  absorptions  of  the  individual 


131] 


IONISATION   BY   RONTGEN   RAYS. 


253 


molecules  in  that  substance,  the  absorption  due  to  any  molecule 
being  independent  of  the  nature  of  the  chemical  compound  of 
which  it  forms  a  part  or  its  physical  state.  Benoist  states  that 
the  absorption  does  not  depend  upon  the  temperature.  The 
absorption  of  a  body  for  the  Rontgen  rays  is  thus  an  additive 
property. 


35 


30 


25 


20 


15 


10 


\Na 


60 


70 


50 


50 


100          150 

Fig.  67. 


200 


0   10  30 


There  is  a  very  close  connection  between  the  absorption  of 
an  element  and  its  molecular  weight ;  this  is  shown  by  the  curve 
in  Fig.  67  (taken  from  Benoist's  paper)  in  which  the  ordinates 


254 


IONISATION   BY   HONTGEN    RAYS. 


[131 


represent  the  equivalents  of  transparency  of  the  elements,  the 
abscissae  the  molecular  weight ;  it  will  be  seen  that  the  curve 
is  quite  a  smooth  one,  in  every  case  the  transparency  diminishes 
as  the  molecular  weight  increases.  From  this  it  follows  that  the 
molecular  absorption  increases  with  the  molecular  weight.  Having 
got  the  curve  connecting  the  transparency  with  the  molecular 
weight,  it  is  evident  that  we  have  the  means  of  determining  its 
molecular  weight  by  measuring  its  transparency  to  Rb'ntgen  rays 
when  in  a  pure  state  or  when  combined  with  elements  whose 
transparency  is  known.  Benoist  has  applied  this  method  to 
determine  the  molecular  weight  of  indium. 

From  Benoist's  results  I  have  calculated  the  following  relative 
values  of  a  for  some  of  the  elements  which  often  occur  in  gaseous 
compounds. 


Substance 

a 

Substance 

a 

O9 

N2 

•36 

•27 

S2 

Clo 

2-8 
4 

C, 

•17 

Br2 

47 

Knowing  a  for  these  gases  we  can  calculate  the  absorptions  of 
the  gases  measured  by  Rutherford  (see  page  250),  the  results  are 
given  in  the  following  table : 


Gas 

a  (Benoist) 

X  (Kutherford) 

o 

•36 

•001 

CO 

•45 

•001 

S02 

1-76 

•0025 

H2S 

1-4 

•0037 

HC1 

2 

•0065 

C12 

4 

•0095 

a/X 


360 
450 
700 
378 
301 
420 


In  calculating  the  numbers  in  the  second  column  I  have 
neglected  the  absorption  due  to  the  hydrogen  in  the  compound, 
as  this  is  too  small  to  be  accurately  determined.  Benoist  showed 
that  the  relative  values  of  a  depended  to  some  extent  upon  the 
nature  of  the  rays ;  taking  this  into  account  Rutherford's  results 
are  in  fair  accordance  with  Benoist's  law  except  in  the  case 
of  S02. 


132]  IGNISATION   BY  RONTGEN   RAYS.  255 

The  question  arises  whether  the  energy  absorbed  by  the  gas  is 
wholly  accounted  for  by  the  work  spent  in  ionising  the  gas  or 
whether  part  of  the  energy  of  the  rays  is  directly  transformed  into 
heat  and  energy  in  the  gas  without  the  intervention  of  ionisation : 
if  the  ions  are  allowed  to  recombine,  the  work  spent  in  ionisation 
will  ultimately  appear  as  heat  energy  in  the  gas;  this  would 
however  not  necessarily  be  the  case  if  the  ions  were  driven  out  of 
the  gas  by  a  strong  electric  field.  The  evidence  is,  I  think,  in 
favour  of  the  view  that  the  ionisation  of  the  gas  is  only  accountable 
for  a  small  part  of  the  loss  of  energy.  Rutherford  and  McClung* 
have  calculated  the  work  necessary  to  ionise  a  molecule  of  the  gas 
on  the  assumption  that  all  the  loss  of  energy  in  the  rays  was  due 
to  the  ionisation  of  the  gas ;  on  this  hypothesis  they  found  the 
work  necessary  to  ionise  a  molecule  of  air  was  equal  to  the  work 
done  on  the  ionic  charge  when  it  fell  through  a  potential  difference 
of  about  175  volts,  this  is  very  much  larger  than  the  value  of  the 
same  quantity,  about  two  volts,  obtained  by  H.  A.  Wilson  and 
Townsend  (see  p.  190)  by  different  considerations.  Combining 
these  results  we  conclude  that  only  about  1/80  of  the  energy  of 
the  rays  is  expended  in  the  ionisation  of  the  gas,  the  rest  being 
converted  into  heat. 

Variation  of  tlie  ionisation  of  a  gas  iviih  the  temperature. 

132.  This  was  investigated  in  the  case  of  air  by  Perrin-f  who 
showed  that  if  the  pressure  of  the  gas  was  kept  constant,  then 
between  the  temperatures  — 12°  and  + 145°  C.  the  total  ionisation 
was  independent  of  the  temperature ;  as  the  density  of  the  gas 
when  the  pressure  is  constant  varies  inversely  as  the  absolute 
temperature,  and,  as  we  have  seen,  the  amount  of  ionisation  is 
proportional  to  the  density,  it  follows  that  the  amount  of  ionisa- 
tion in  a  given  mass  of  gas  is  directly  proportional  to  the  absolute 
temperature. 

It  is  very  desirable  that  further  experiments  should  be  made 
on  the  variation  of  the  ionisation  of  different  gases  with  the 
temperature,  as  this  variation  has  a  direct  bearing  on  the  question 
as  to  what  is  the  condition  of  the  molecules  which  are  ionised 
by  the  Rontgen  rays.  We  must  remember  that  it  is  only  an 

*  Rutherford  and  McClung,  Phil.  Trans,  cxcvi.  p.  25,  1901. 

t  Perrin,  Annales  de  Chimie  et  de  Physique  [7],  xi.  p.  496,  1897. 


256  IONISATION   BY   RONTGEN   RAYS.  [132 

exceedingly  small  fraction  of  the  molecules  which  are  ionised  by 
the  rays  ;  even  when  the  ionisation  is  exceptionally  large  the  pro- 
portion of  the  number  of  free  ions  to  the  number  of  molecules  of 
the  gas  is  less  than  1  to  1012.  Thus  if  all  the  molecules  of  the  gas 
are  equally  exposed  to  the  rays,  since  the  ionisation  is  confined  to 
an  exceedingly  small  fraction  of  the  number  of  molecules  the 
molecules  which  are  ionised  must  be  in  some  state  very  far 
removed  from  the  average  condition  of  the  molecules.  One  sup- 
position which  naturally  suggests  itself  is  that  it  is  only  those 
molecules  which  possess  an  amount  of  kinetic  energy  exceeding 
a  certain  value  which  get  ionised  by  the  rays  :  the  following  in- 
vestigation however  shows  that  in  this  case  the  ionisation  ought 
to  vary  much  more  rapidly  with  the  temperature  than  is  consistent 
with  Perrin's  results. 

For  according  to  the  Kinetic  Theory  of  Gases  the  number  of 
molecules  in  a  cubic  centimetre  which  have  velocities  between 
c  and  c  +  dc  is  equal  to 


VTT 

where  N  is  the  whole  number  of  molecules  per  unit  volume,  6 
the  absolute  temperature  and  m  the  mass  of  a  molecule  of  the  gas, 
hence  if  n  is  the  number  of  molecules  which  have  velocities 
greater  than  c, 

.  ,00     _m£ 

n=-^N0-*       e    '   c*dc, 

V  7T  Jet 

or  putting  c2  =  0o>2, 

4         f°° 

n  =  -~N\     e-^tfdw; 
VTT      J  £, 
V* 

hence  we  have 

dn_    2        -¥* 
M-fir*  -&' 

Now  since  the  number  of  molecules  ionised  is  an  exceedingly 
small  fraction  of  n,  if  these  are  the  molecules  having  a  velocity 

_mc? 

greater  than  c1}  then  e  9  must  be  very  small,  but  when  this  is 
the  case  dn/dd  will  increase  very  rapidly  with  0;  thus  suppose 

me? 

for  a  moment  that  e     0    is  equal  to  10~12,  then  if  we  double  6  the 


132]  IONISATION    BY   RONTGEN    RAYS.  257 

value  of  dn/dO  at  the  higher  temperature  would  be  about  120,000 
times  its  value  at  the  lower,  while  according  to  Perrin's  result  the 
temperature  coefficient  of  the  ionisation  is  constant :  hence  we 
conclude  that  the  few  molecules  that  are  ionised  cannot  owe  their 
ionisation  to  the  possession  of  an  abnormal  amount  of  kinetic 
energy;  a  similar  objection  would  apply  to  the  ionisation  being 
due  to  any  property  of  the  molecule  whose  frequency  was  given  by 
the  Max  well- Bolt  zmann  Law  of  Distribution. 

Another  view  that  at  first  sight  appears  as  if  it  might  explain 
the  small  amount  of  ionisation  is  that  this  is  not  due  to  the  direct 
action  of  the  Rontgen  rays  on  the  molecules,  but  that  these  rays 
act  on  the  free  ions,  which  as  the  phenomenon  of  spontaneous 
ionisation  shows  are  always  present  in  small  numbers,  even  when 
the  gas  is  in  its  normal  state ;  the  rays  giving  to  these  ions  sufficient 
kinetic  energy  to  enable  them  to  ionise  the  molecules  of  the  gas 
against  which  they  strike.  To  express  the  results  of  this  hypothesis 
in  an  analytical  form,  let  us  suppose  that  the  number  of  free  positive 
or  negative  ions  per  cubic  centimetre  is  n,  and  that  in  consequence 
of  the  kinetic  energy  given  by  the  rays  to  an  ion,  each  ion 
produces  o>  other  ions  per  second,  let  the  number  of  ions  which 
recombine  in  one  second  be  cm2,  and  let  (3  be  the  number  of  ions 
produced  per  second  from  the  spontaneous  ionisation  of  the  gas, 
then  when  things  are  in  a  steady  state  we  have 

o>??  +/3-cw2=0, 


'8      a)2 
or  n.-_  ._  + 


-f+v- 

'la.      v    a 


Since  the  number  of  ions  produced  by  the  rays  is  large  compared 
with  that — V/3/a — due  to  the  spontaneous  ionisation  @/a  must 
be  small  compared  with  o>2/4a2,  and  we  have  approximately  n  =  w/a, 
thus  we  should  have  a  definite  value  for  the  number  of  ions  in  i 
cubic  centimetre  of  the  gas.  This  view  however  leads  to  a  result 
which  is  not  in  accordance  with  the  results  of  observation,  for  the 
saturation  current  for  a  cubic  centimetre  of  the  gas  is  proportional 
to  the  number  of  ions  produced  in  one  second  in  a  cubic  centi- 
metre of  the  gas,  i.e.  con.  Now  this  number  being  proportional  to  n, 
the  number  of  free  ions,  should  be  less  in  a  strong  electric  field 
than  in  a  weak  one,  for  in  a  strong  field  the  life  of  the  ion  is 
shorter  than  it  is  in  a  weak  one,  as  it  is  rapidly  driven  out  of  the 
T.  G.  17 


258  IONISATION   BY   RONTGEN   KAYS.  [133 

gas  against  the  electrodes ;  hence  if  the  view  we  are  discussing 
were  the  true  one,  the  current  through  a  gas  when  the  electric 
field  is  strong  ought  to  diminish  as  the  strength  of  the  field 
increases ;  as  this  is  not  the  case  we  conclude  that  the  ionisation 
cannot  be  produced  in  the  way  we  have  been  considering. 

Other  possible  explanations  of  the  small  number  of  molecules 
dissociated  by  the  rays  are  (1)  that  the  rays  are  of  such  a  kind 
that  only  a  small  fraction  of  the  molecules  are  exposed  to  the  full 
force  of  their  influence :  that  if  for  example  we  consider  a  plane 
at  right  angles  to  the  direction  of  propagation  of  the  rays  the 
energy  is  not  distributed  uniformly  over  this  plane,  but  that  the 
distribution  of  energy  has  as  it  were  a  structure,  although  an 
exceedingly  fine  one,  places  where  the  energy  is  large  alternating 
with  places  where  it  is  small,  like  the  mortar  and  bricks  in  a  wall ; 
thus  if  the  places  where  the  energy  is  intense  enough  to  produce 
ionisation  of  a  molecule  occupied  but  a  small  fraction  of  the  area 
of  the  plane  at  right  angles  to  the  rays,  the  rays  would  be  able  to 
pass  through  a  gas  and  yet  only  a  small  fraction  of  the  molecules 
would  be  exposed  to  their  maximum  influence,  just  as  is  the  case 
when  a  beam  of  cathode  rays  passes  through  the  gas ;  we  shall 
return  to  this  point  when  we  consider  the  nature  of  the  Rontgen 
rays.  Another  view  which  might  be  taken  is  that  all  the  molecules 
of  a  gas,  even  though  this  gas  may  be  like  hydrogen  an  element,, 
are  not  of  the  same  kind,  and  that  mixed  with  the  ordinary  mole- 
cules we  have  a  few  which  are  of  such  a  kind  as  to  be  very  easily 
ionised,  and  that  the  number  of  molecules  of  this  kind,  which 
are  practically  molecules  of  a  different  gas,  is  not  given  by 
Maxwell's  law  of  distribution.  The  idea  that  even  a  gas  is  not 
uniform  in  composition,  but  contains,  as  it  were  mixed  with  it,. 
small  quantities  of  other  gases — not  necessarily  as  impurities  due 
to  its  method  of  preparation  but  as  an  essential  constituent  of  it — 
may  appear  at  first  stating  so  opposed  to  the  ordinary  facts  of 
chemistry  as  not  to  be  worthy  of  discussion.  We  may  however 
point  out  that  the  quantities  of  such  gases,  if  we  may  take  the 
ionisation  as  their  measure,  are  so  small  as  to  be  utterly  beyond 
the  power  of  chemical  analysis  to  detect,  so  that  it  cannot  be 
by  chemical  considerations  that  the  truth  or  falsehood  of  this 
hypothesis  can  be  decided. 

133.  Secondary  Rontgen  radiation.  When  the  Rontgen  rays 
pass  through  a  substance  they  cause  it  to  emit  Rontgen  rays — 


13:3] 


IONISATION   BY   RONTGEN    RAYS. 


259 


called  secondary  rays — which  in  many  cases  at  any  rate  are  different 
in  character  from  the  rays— primary  rays — which  produced  them. 
These  secondary  rays  are  produced  by  solids,  liquids  and  gases. 
Perrin*  observed  that  when  the  rays  struck  a  metal  plate,  more 
ionisation  was  produced  than  if  rays  of  the  same  intensity  passed 
through  the  air  without  coming  into  contact  with  the  plate.  He 
arranged  two  pairs  of  parallel  plates  so  that  the  same  volume  of 
gas  was  exposed  to  rays  of  the  same  intensity  between  each  pair 
of  plates,  in  the  one  pair  however  the  rays  passed  between  the 
plates  without  touching  the  metal,  while  in  the  second  pair  the 
rays  were  incident  normally  on  one  of  the  plates ;  he  found  that 
the  saturation  current  was  always  greater  for  the  second  pair  of 
plates  than  for  the  first,  the  excess  depending  on  the  metal  struck 
by  the  rays.  If  this  plate  were  made  of  gold,  zinc,  lead  or  tin, 
the  difference  was  considerable,  if  it  was  made  of  aluminium  it 
was  only  small,  while  it  was  quite  inappreciable  if  the  plate  were 
wet  with  water,  alcohol  or  petroleum. 


Fig.  68. 

Sagnacf  has  made  some  experiments  which  show  very  clearly 
the  existence  of  these  secondary  rays;  the  method  he  used  is 
shown  in  Fig.  68  a  and  j3 ;  in  the  experiment  represented  in 

*  Perrin,  Annales  de  Chimie  et  de  Physique  [7],  xi.  p.  496,  1897. 
t  Sagnac,  ibid.  [7],  xxii.  p.  493,  1901. 

17—2 


260 


IONISAT10N   BY   KONTGEN   RAYS. 


[134 


Fig.  68  a  the  secondary  rays  were  detected  by  their  action  on  a 
photographic  plate,  in  that  represented  in  Fig.  68  ft  by  their  action 
in  discharging  a  gold-leaf  electroscope.  L  is  the  bulb  producing 
the  primary  rays,  EE  a  thick  lead  plate  to  screen  off  these  rays 
from  the  photographic  plate  or  the  electroscope,  MM  the  plate 
struck  by  the  primary  rays  and  emitting  the  secondary  ones,  ee  in 
Fig.  68  a  the  photographic  plate ;  the  electroscope  is  covered  with 
a  metal  case  connected  with  earth  to  screen  off  from  the  gas 
exposed  to  the  primary  rays  the  electric  field  due  to  the  charged 
gold-leaves,  the  secondary  rays  entered  this  case  through  a  thin 
aluminium  window.  The  electroscope  was  discharged  and  the 
plate  affected  even  when  MM  was  made  of  comparatively  light 
and  transparent  substances,  such  as  paraffin,  ebonite,  sulphur,  or 
aluminium,  while  a  greater  effect  was  produced  by  heavy  sub- 
stances. A  small  effect  is  produced  even  when  the  plate  MM  is 
absent,  this  is  due  to  the  secondary  rays  emitted  by  the  air ;  the 
secondary  rays  emitted  by  air  were  first  observed  by  Rontgen* 
who  detected  them  by  the  luminosity  they  produced  in  a  phos- 
phorescent screen. 


134.  Sagnac  (loc.  cit.)  showed  that  the  secondary  rays  were  not 
diffusely  reflected  primary  rays ;  he  did  this  by  proving  that  the 
secondary  rays  were  much  more  easily  absorbed  than  the  primary 
ones.  The  method  he  used  for  this  purpose  is  shown  in  Fig.  69. 
The  primary  rays  from  the  bulb  I  passed  through  two  openings 

*  Eontgen,  Wied.  Ann.  Ixiv.  p.  18,  1898. 


135]  IONISATION   BY   RONTGEN   RAYS.  261 

ab,  cd  in  the  lead  plates  E1E1,  E2E2,  the  secondary  rays  from  the 
plate  LL  passed  through  a  hole  in  a  lead  plate  E^E^,  then  through 
a  thin  aluminium  window  into  the  electroscope  G.  A  plate  of 
aluminium  AA  is  placed  first  in  the  path  of  the  primary  rays  and 
the  rate  of  leak  observed,  it  is  then  removed  from  the  path  of  the 
primary  rays  and  placed  at  A! A'  in  the  path  of  the  secondary 
rays,  and  the  rate  of  leak  again  observed ;  the  rate  of  leak  in  the 
latter  case  is  always  less  than  that  in  the  former,  showing  that  the 
secondary  rays  are  more  absorbed  by  the  plate  than  the  primary 
ones.  If  t  is  the  time  taken  by  the  gold-leaves  to  fall  through  a 
certain  angle  when  the  plate  is  at  AA,  tf  the  time  when  the  plate 
is  at  A' A',  then  if  c  =  (t'  —  t)/t,  c  is  called  by  Sagnac  the  coefficient 
of  transformation  of  the  rays.  This  coefficient  depends  upon  the 
nature  of  the  plate  LL;  it  is  much  smaller  when  the  plate  is  made 
of  light  substances  such  as  aluminium  or  paraffin  than  when  it  is 
made  of  heavy  ones  such  as  gold  or  lead :  this  shows  that  the 
secondary  rays  emitted  by  light  substances,  although  not  so 
numerous,  are  more  penetrating  than  those  emitted  by  heavy  ones. 
Sagnac  also  showed  that  when  the  distance  of  the  electroscope 
from  the  plate  LL  was  increased,  a  much  greater  diminution  was 
produced  in  the  rate  of  leak  when  the  plate  LL  was  made  of  lead 
than  when  it  was  made  of  zinc  or  copper,  showing  that  a  con- 
siderable proportion  of  the  secondary  rays  from  lead  were  absorbed 
by  a  few  centimetres  of  air. 

135.  Some  very  interesting  experiments  on  the  secondary 
rays  were  made  by  Townsend*  who  used  the  method  represented 
in  Fig.  70.  The  bulb  producing  the  rays  and  the  induction  coil 
by  which  it  was  worked  were  placed  inside  a  box  covered  with 
lead,  having  one  aperture  at  A  through  which  the  rays  passed  up 
through  a  lead  tube  to  prevent  them  from  spreading  out  laterally. 
C  is  a  cylinder  of  wire-gauze  containing  an  axial  electrode  0. 
The  gauze  was  connected  with  one  terminal  of  a  battery  of  small 
storage  cells,  the  other  terminal  of  which  was  put  to  earth,  the 
electrode  G  was  connected  with  an  insulated  pair  of  quadrants  of 
an  electrometer.  The  potential  difference  between  the  gauze  and 
the  electrode  G,  85  volts,  was  sufficient  to  produce  the  saturation 
current.  The  substance  emitting  the  secondary  radiation  was 
placed  at  D  and  measurements  were  made  (1)  when  the  secondary 

*  J.  S.  Townsend,  Proc.  Camb.  Phil.  Soc.  x.  p.  217,  1899. 


262 


IONISATION   BY   RONTGEN   RAYS. 


[135 


radiation  passed   through   nothing  but  air,  (2)   when   it  passed 
through  a  plate  of  aluminium  '25mm.  thick.      The  results  are 


Fig.  70. 

contained  in  the  following  table,  the  numbers  being  the  deflection 
of  the  electrometer  in  10  seconds  : 


Radiator 
(substance 
placed  at  D) 

Rays 
passing 
through 
Air 

Rays 
passing 
through 
Al 

Radiator 
(substance 
placed  at  D) 

Rays 
passing 
through 
Air 

Rays 
passing 
through 
Al 

Air  

2 

1 

Solid  Paraffin 

30 

15-5 

Aluminium  . 

6 

3'5 

Brass   

66 

2-5 

Glass 

7-5 

3 

Zinc  

68 

3 

Lead    . 

24 

6 

70 

2-5 

This  table  shows  very  clearly  the  different  kinds  of  radiation 
given  out  by  different  substances,  thus  the  radiation  from  brass, 
zinc,  and  copper  is  almost  completely  stopped  by  the  aluminium 
while  the  radiation  from  other  substances  passes  through  it  com- 
paratively easily.  The  secondary  radiation  was  found  not  to  be 
much  affected  by  the  state  of  the  surface  of  the  body,  thus  the 
radiation  from  polished  brass  was  only  2  or  3  per  cent,  greater 
than  from  brass  coated  with  oxide :  if  the  brass  was  covered  with 
wet  filter-paper  the  deflection  of  the  electrometer  was  reduced 
from  66  to  46.  The  secondary  radiation  is  not  merely  a  surface 
effect,  the  radiation  comes  from  a  layer  of  the  substance  of  appre- 
ciable thickness.  This  was  proved  by  covering  a  plate  of  aluminium 


135] 


IONISATION    BY    RONTGEN    RAYS. 


263 


with  a  thin  layer  of  paraffin ;  the  radiation  was  reduced  to  about 
one-sixth  of  the  amount  from  a  solid  block  of  paraffin.  With  denser 
substances  such  as  lead  the  layer  from  which  the  secondary  radia- 
tion comes  will  be  much  thinner  than  for  a  light  substance  like 
paraffin.  In  the  first  place  the  primary  rays  can  only  penetrate  to 
a  very  small  depth  below  the  surface,  and  in  the  second  place  the 
secondary  rays  being  so  much  more  easily  absorbed  will  only  be 
able  to  pass  through  a  small  fraction  of  the  thickness  penetrated 
by  the  primary  rays.  Thus  the  thickness  of  the  layer  from  which 
the  radiation  comes  will  always  be  much  less  than  the  thickness 
which  can  be  penetrated  by  the  primary  rays.  The  arrangements 
in  the  preceding  experiments  were  such  that  the  only  radiation 
which  would  affect  the  electrometer  was  that  which  had  passed 
through  several  centimetres  of  air.  Townsend  showed  that  in 
addition  to  this  there  was  also  secondary  radiation  which  was 
absorbed  by  a  layer  of  air  a  few  millimetres  thick. 

The  arrangement  used  for  this  purpose  is  shown  in  Fig.  71. 
It  was  arranged  to  find  the  saturation-current  between  two 
circular  plates  A  and  B,  4'8  cm.  radius,  for  different  distances 


Fig.  71. 


between   the  plates ;   if  there  were  no  secondary  radiation  this 
current  would  be  proportional  to  these  distances. 

The  primary  rays  passed  through  a  hole  M  in  a  lead  plate  and 
then  through  a  hole  N  in  another  lead  plate  on  which  the  lower 


264 


IONISATION   BY   RONTGEN   RAYS. 


[135 


plate  BB,  which  was  made  of  aluminium,  rested.  After  passing 
through  N  the  primary  rays  passed  through  the  air  and  fell  on 
the  plate  A  A,  whose  distance  from  B  could  be  adjusted  by  means 
of  a  screw.  A  series  of  experiments  were  made  with  plates  of 
different  materials  at  A,  the  plate  B  was  an  aluminium  one 
throughout  the  experiments ;  the  results  of  the  experiments  are 
given  in  the  following  table  :  t  is  the  distance  between  the  plates 
in  millimetres,  and  the  numbers  in  the  other  columns  are  propor- 
tional to  the  saturation-currents  in  the  various  cases.  The 
composition  of  the  upper  plate  is  given  in  the  first  row  in  the 
table. 


t 

Brass 

Cu 

Zn 

Al 

1 

55 

54-4 

49 

15 

2 

81 

84 

66 

23-7 

5 

109-5 

107-5 

87 

40-8 

10 

126 

128 

103 

57 

15 

142 

144 

119 

73 

If  there  were  no  secondary  radiation  the  2,  3,  4  and  5  columns 
should  be  identical,  and  the  numbers  proportional  to  the  distance 
between  the  plates.  Let  us  take  the  case  of  brass,  then  when  the 
distance  between  the  plates  is  15  mm.,  the  number  of  ions  pro- 
duced is  proportional  to  142;  when  the  distance  between  the  plates 
is  reduced  to  one  millimetre,  the  number  of  ions  is  not  reduced  to 
1/15  but  to  l/2'6  only,  showing  that  there  are  relatively  a  great 
many  more  ions  in  the  millimetre  of  air  next  the  brass  plate  than 
there  are  in  the  layers  of  air  at  a  considerable  distance  away  from 
it.  We  see  from  the  table  that  the  ionisation  in  the  millimetre 
of  air  nearest  the  metal  is  proportional  to  55,  in  the  next  milli- 
metre it  is  26,  the  average  in  the  next  three  millimetres  is  9'5, 
in  the  next  five  3*5,  and  in  the  last  five  3'2  :  thus  by  far  the  greater 
part  of  the  secondary  radiation  is  absorbed  by  a  layer  of  air  2  milli- 
metres thick,  this  part  of  the  radiation  would  be  all  absorbed  by 
the  air  between  the  plate  and  the  cylinder  in  the  experiment 
shown  in  Fig.  70,  so  that  the  numbers  obtained  by  the  use  of 
this  instrument  relate  to  a  different  class  of  rays  from  those 
detected  by  the  parallel  plates.  The  curves  in  Fig.  ?2,  taken 
from  Townsend's  paper,  give  a  good  idea  of  the  rapidity  with 


136] 


IONISATION    BY    RONTGEN    RAYS. 


265 


which  the  ionisation  diminishes  as  the  distance  from  the  metal 
surface  increases ;  the  ordiriates  in  the  curves  are  proportional  to 
the  total  amount  of  ionisation  up  to  a  distance  from  the  plate 
represented  by  the  abscissae.  If  S  is  the  ratio  of  the  number  of 
ions  produced  by  the  easily  absorbable  secondary  rays  in  the  air  to 
the  number  of  ions  produced  by  the  primary  rays  when  they 
traverse  a  layer  of  air  1  cm.  thick,  then  Townsend  found  that  for 


ao 


6Q 


Fig.  72. 

copper  S  =  2'o,  for  zinc  S=l'84i,  for  aluminium  $  =  '4:  these 
numbers  are  considerably  larger  than  those  previously  obtained 
by  Perrin,  and  this  and  the  difference  between  these  results 
and  those  obtained  by  Sagnac  indicate  that  the  character  of 
the  secondary  radiation  depends  very  largely  upon  that  of  the 
primary.  H.  S.  Allen*  has  compared  the  number  of  ions  produced 
by  the  secondary  ionisation  with  those  which  would  be  produced 
if  the  primary  rays  were  entirely  absorbed  by  the  gas ;  using  brass 
as  the  metal  and  sulphuretted  hydrogen  as  the  gas,  he  found  that 
the  number  of  ions  produced  by  the  secondary  radiation  was  about 
1/2000  of  the  number  which  would  have  been  produced  if  the 
primary  rays  had  been  absorbed  by  the  sulphuretted  hydrogen. 

136.  The  effect  of  the  secondary  ionisation  has  to  be  taken 
into  account  in  all  investigations  on  the  relation  between  the 
ionisation  and  the  pressure.  Thus  suppose  we  were  investigating 
the  relation  between  the  saturation-current  and  the  pressure,  the 


H.  S.  Allen,  Phil.  Mag.  vi.  3,  p.  126,  1902. 


266  IONISATION   BY   RONTGEN   RAYS.  [137 

current  passing  between  two  parallel  plates,  one  of  these  being 
exposed  to  the  primary  rays  and  giving  out  secondary  radiation. 
The  secondary  radiation  is  absorbed  within  a  short  distance  from 
the  plate,  and  though  when  we  diminish  the  pressure  we  increase 
this  distance  the  total  amount  of  ionisation  will  not  be  affected 
until  the  pressure  gets  so  low  that  the  secondary  rays  can  travel 
from  one  plate  to  the  other.  Thus  if  S  is  the  secondary  and  P 
the  primary  ionisation,  the  latter  is  proportional  to  the  pressure  p, 
equal  say  to  cap,  then,  until  the  pressure  gets  so  low  that  the 
secondary  radiation  extends  from  one  plate  to  the  other,  the  satu- 
ration-current will  be  proportional  to  S  +  ap ;  thus  if  the  secondary 
ionisation  is  large  compared  with  the  primary,  there  will  be  at  first 
very  little  change  in  the  saturation-current  due  to  a  change  in 
pressure;  when  the  pressure  gets  so  low  that  the  secondary 
radiation  is  not  nearly  absorbed  between  the  plates,  then  both 
secondary  ionisation  and  primary  ionisation,  and  therefore  the 
saturation-current,  will  be  proportional  to  the  pressures. 

137.  A  metal  plate  when  struck  by  Rontgen  rays  emits,  in 
addition  to  the  easily  absorbed  secondary  radiation,  negatively 
electrified  particles,  or,  as  we  may  express  it,  the  metal  gives  out 
cathode  as  well  as  Rontgen  rays.  The  cathode  rays  can  be  distin- 
guished from  the  others  by  being  deflected  by  a  magnetic  field, 
and  by  carrying  with  them  a  charge  of  negative  electricity  so  that 
the  metal  plate  from  which  they  start  would,  if  insulated,  acquire 
a  charge  of  positive  electricity.  Dorn*  has  shown  that  rays  which 
can  be  deflected  by  a  magnet  are  emitted  by  plates  of  lead  and 
platinum,  and  to  a  smaller  extent  by  plates  of  copper  and  zinc 
when  exposed  to  Rontgen  rays.  The  direction  of  the  deflection 
is  the  same  as  that  of  cathode  rays  coming  from  the  metal.  Curie 
and  Sagnac  f  have  shown  that  the  metal  plate  emits  negative 
electricity  and  acquires  a  positive  charge;  in  order  to  demonstrate 
this  effect  it  is  necessary  to  work  in  a  good  vacuum,  as  if  the 
plate  is  surrounded  by  air  at  an  appreciable  pressure,  the  con- 
ductivity of  the  air  due  to  the  primary  and  secondary  radiations  is 
so  great  that  any  charge  on  the  plate  leaks  away  before  it  can  be 
observed.  One  of  the  methods  used  by  Curie  and  Sagnac  to 
demonstrate  the  charge  on  the  plate  is  shown  in  Fig.  73. 

*  Dorn,  Abhand.  d.  naturf.  Ges.  zu  Halle,  xxii.  p.  39,  1900,  Beiblatter,  24,  p.  572. 
t  Curie  and  Sagnac,  Journal  de  Physique,  [4],  i.  p.  13,  1902. 


137] 


IONISATION   BY   RONTGEN   RAYS. 


267 


A  thin  piece  of  metal  M  is  insulated  and  connected  with  one 
pair  of  quadrants  of  an  electrometer;  M  is  enclosed  in  a  metal 
box  ABCD  which  is  connected  with  the  earth,  the  lower  face 
of  the  box  is  pierced  with  windows  closed  with  thin  foil  of  the 
same  material  as  the  box ;  the  bulb  I  which  produces  the  rays  is 
enclosed  in  a  box  covered  with  lead.  When  the  plate  M  and  the 
box  ABCD  are  made  of  different  metals,  then  at  atmospheric 
pressure  the  conductivity  of  the  air  is  considerable,  and  the 
arrangement  acts  like  a  galvanic  battery,  a  potential  difference 
equal  to  the  contact  difference  of  potential  being  established 
between  M  and  the  box;  as  we  exhaust  the  air  from  the  box  this 


meter 


Fig.   73. 

difference  remains  at  first  unaltered,  but  when  a  very  good  vacuum 
is  obtained  the  potential  difference  is  greatly  increased;  thus  when 
the  plate  M  is  made  of  platinum  and  the  box  of  aluminium,  Curie 
and  Sagnac  found  that  at  atmospheric  pressure  M  was  positive  to 
the  box  by  less  than  1  volt,  but  at  a  high  vacuum  the  potential  of 
M  was  greater  than  that  of  the  box  by  about  30  volts.  This 
shows  that  the  platinum  emits  more  negative  electricity  than  it 
receives  from  the  aluminium.  If  the  plate  M  is  aluminium,  and 
the  box  platinum,  the  plate  acquired  a  negative  charge.  Curie 
and  Sagnac  showed  that  the  penetrating  power  of  these  negatively 
charged  rays  was  of  the  same  order  as  that  of  the  Lenard  rays, 
a  piece  of  aluminium  foil  about  '46  x  10~6  cm.  thick  reducing 
the  stream  of  negative  electricity  about  40  per  cent.:  from  this  we 


268  IONISATION   BY   RONTGEN   RAYS.  [138 

may  conclude  that  the  velocity  of  the  secondary  rays  is  of  the 
same  order  as  that  of  cathode  rays  in  a  highly  exhausted  tube, 
say  between  109  and  1010  cm. /sec.  Dorn*  has  measured  the  mag- 
netic deflection  of  these  rays  and  finds  velocities  varying  from 
1'8  x  109  to  8*5  x  109  cm./sec.,  the  values  depending  upon  that 
assumed  for  e/m. 

We  may  compare  the  effects  produced  when  Rontgen  rays  fall 
on  a  metal  plate  with  those  produced  by  the  incidence  of  ultra- 
violet light ;  in  both  cases  cathode  rays  are  emitted  by  the  metal. 
The  secondary  Rontgen  rays  may  be  compared  with  the  reflected 
light  or  perhaps  with  greater  accuracy  with  the  phosphorescent 
light  given  out  by  certain  substances  under  the  influence  of 
ultra-violet  light,  for  which  the  reflected  light  is  of  the  same 
quality  as  the  incident  light ;  the  secondary  Rontgen  rays  are  not 
of  the  same  nature  as  the  primary  rays,  part  at  least  of  the 
secondary  rays  being  much  more  easily  absorbed  than  the 
primary  ones. 

On  account  of  the  great  absorption  of  the  secondary  and 
cathode  rays,  the  layer  from  which  they  come  must  be  very 
close  to  the  surface  :  thus  suppose  AB  is  the  face  of  a  metal 
plate  on  which  Rontgen  rays  are  incident,  let  the  primary  rays 
penetrate  to  CD,  then  all  the  metal  between  AB  and  CD  will  be 
emitting  secondary  and  cathode  rays,  but  it  is  only  the  secondary 
rays  which  come  from  a  thin  layer  ABEF  which  escape  extinc- 
tion before  reaching  the  surface,  and  as  the  cathode  rays  are  still 
more  easily  absorbed  it  is  only  those  from  a  still  thinner  layer 
ABE'F'  which  emerge  into  the  air. 

138.  Theory  of  the  Secondary  Radiation.  The  secondary 
radiation  is  readily  explained  if  we  take  the  view,  which  we  shall 
discuss  later,  that  the  Rontgen  rays  consist  of  exceedingly  thin 
pulses  of  very  intense  electric  and  magnetic  force.  Let  us  suppose 
that  such  a  pulse  is  travelling  through  a  medium  containing  ions — 
it  is  not  necessary  that  the  ions  should  be  free :  when  the  pulse 
reaches  a  charged  ion  the  ion  will  be  acted  on  by  a  very  intense 
force  and  its  motion  accelerated.  Now  when  the  velocity  of  a 
charged  body  is  changing  pulses  of  electric  and  magnetic  force 
proceed  from  the  body,  the  magnitude  of  these  forces  being  pro- 

*  Dorn,  Lorentz  Jubilee  volume,  p.  595,  1900. 


138]  IONISATION   BY   RONTGEN   RAYS.  269 

portional  to  the  acceleration  of  the  body  :  thus  while  the  primary 
Rontgen  pulse  is  passing  over  the  ion  and  accelerating  its  motion, 
the  ion  gives  out  a  pulse  of  electric  and  magnetic  force  —  the 
secondary  Rontgen  pulse  —  the  secondary  pulse  ceasing  as  soon 
as  the  acceleration  of  the  ion  vanishes,  i.e.  as  soon  as  the  primary 
pulse  has  passed  over.  It  is  easy  to  compare  the  energy  in  the 
secondary  pulse  with  that  in  the  primary.  For  suppose  the  ion  0 
is  moving  parallel  to  the  axis  of  a?,  let  /  be  its  acceleration,  then 
the  ion  emits  a  pulse  of  magnetic  force  such  that  when  the 
pulse  reaches  the  point  P,  the  magnitude  of  the  force  is  equal  to 
fe  sin  6  1  V.  OP,  V  being  the  velocity  of  light,  6  the  angle  be- 
tween OP  and  the  axis  of  as,  and  e  the  charge  on  the  ion  in 
electromagnetic  units  ;  the  direction  of  the  force  is  at  right  angles 
to  OP  and  the  axis  of  x  ;  this  magnetic  force  is  accompanied  by 
an  electric  force  at  right  angles  to  OP  in  the  plane  containing  OP 
and  the  axis  of  x,  and  equal  in  magnitude  to  fe  sin  6  /OP:  hence  by 
Poynting's  theorem  the  flow  of  energy  is  along  OP,  and  since  the 
quantity  of  energy  flowing  across  unit  area  in  unit  time  is,  when 
as  in  this  case  the  electric  and  magnetic  forces  are  at  right  angles 
to  each  other,  equal  to  the  product  of  the  electric  and  magnetic 
forces  divided  by  4-7T,  the  rate  at  which  energy  flows  across  unit 
surface  is  equal  to 


47T 

integrating  this  expression  over  the  surface  of  a  sphere  with  the 
ion  as  centre,  we  see  that  the  rate  at  which  energy  is  leaving  the 
ion  is  equal  to 

1  &f* 

3    V  ' 
and  the  total  amount  of  energy  emitted  by  the  ion  is  equal  to 


i  p1*  r 
I  V  //* 


Now  suppose  that  the  electric  force  in  the  primary  Rontgen 
pulse  is  parallel  to  x  and  equal  to  X,  then  if  in  is  the  mass  of  the 

ion  /=  — ;  substituting  this  expression  for  /  we  find  that  the 
energy  emitted  by  the  ion  is  equal  to 


270  IONISATION   BY   RONTGEN   RAYS.  [138 

the  integration  extending  over  the  time  taken  by  the  pulse  to 
pass  over  the  ion ;  if  d  is  the  thickness  of  the  pulse  and  if  X  is 
constant  from  the  front  to  the  back  of  it,  then 


V 

and  thus  the  total  energy  in  the  secondary  radiation  emitted  by 
the  ion  is  equal  to 

l^X^d 

3  ra2  T2  ' 
if  E  is  the  energy  per  unit  area  of  the  pulse,  then 


-. 

47T      F2    ' 

thus  the  energy  emitted  by  the  ion  is  equal  to 

47T     # 

3    m*E> 

and   if  there   are  N  ions   per   unit   volume  the   energy  of  the 
secondary  radiation  per  unit  volume  is 


3      77? 

Though  each  pulse  of  secondary  radiation  given  out  by  an  ion 
is  of  the  same  thickness  as  the  primary  pulse,  yet  the  properties 
of  the  secondary  radiation  may  be  very  different  from  those  of  the 
primary,  for  each  pulse  of  primary  radiation  causes  each  ion  to 
emit  a  pulse  of  secondary  radiation,  so  that  the  single  primary 
pulse  produces  a  great  number  of  secondary  pulses  following  each 
other  at  intervals  which  depend  upon  the  proximity  of  the  ions  in 
the  medium  traversed  by  the  primary  waves  ;  the  properties  of 
this  train  of  pulses  would  depend  upon  X  the  average  distance 
between  the  ions  :  they  would  approximate  to  those  of  light  of 
wave-length  X  and  might  thus  differ  materially  from  those  of  the 
primary  rays.  In  fact  on  this  point  of  view  there  is  much  the 
same  difference  between  the  primary  and  secondary  rays,  as  there 
is  between  the  sharp  crack  of  lightning  and  the  prolonged  roll  of 
thunder. 

We  see  from  the  preceding  equations  that  in  passing  over 
a  distance  dx,  the  primary  pulse  causes  the  ions  to  emit  secondary 
radiation  whose  energy  is 


138]  IONISATION   BY   RONTGEN   RAYS.  271 

if  this  were  the  only  loss  of  energy  experienced  by  the  primary 
rays,  we  should  have 


,  „         4-7T          „  , 
dE  =  —  0          Edx, 
3    w2 


or  E=Ce~s  «*    , 

so  that  the  opacity  of  the  substance  to  the  primary  rays  would  be 
measured  by 

47T 


this  is  independent  of  d,  the  thickness  of  the  pulse,  and  depends 
merely  upon  the  medium  and  not  upon  the  kind  of  rays  passing 
through  it :  the  very  great  difference  between  the  penetrating 
power  of  hard  and  soft  rays  shows  that  the  energy  spent  in  the 
secondary  radiation  cannot  be  the  chief  cause  of  the  absorption  of 
the  primary  rays.  Another  source  of  loss  of  energy  is  the  energy 
given  to  the  ions  and  retained  by  them :  the  energy  of  the 
secondary  rays  is  energy  radiated  from  the  ions,  but  in  addition  to 
this  energy  the  ions  under  the  action  of  the  rays  retain  an  amount 
of  energy  which  is  large  compared  with  the  energy  they  give  out 
as  radiant  energy.  To  calculate  the  energy  acquired  by  the  ions 
from  the  primary  Rontgen  radiation,  we  regard  that  radiation  as 
consisting  of  a  succession  of  pulses.  In  some  of  these  the  electric 
force  is  in  one  direction,  in  others  in  the  opposite,  and  we  suppose 
that  there  are  as  many  pulses  with  the  force  in  one  direction  as 
there  are  with  the  force  in  the  opposite. 

Let  us  consider  the  effect  produced  on  an  ion  when  a  pair  of 
pulses,  one  positive  and  the  other  negative,  pass  over  it.  Let 
X,  —  X  be  respectively  the  electric  forces  in  the  positive  and 
negative  pulses,  d  the  thickness  of  either  pulse,  D  the  distance 
between  the  pulses;  then  the  positive  pulse  gives  to  the  ion  a 
velocity  Xed/Vm,  and  the  ion  on  the  arrival  of  the  second  pulse 
will  have  moved  through  a  distance  (Xed/Vm)  (D/V)  (if  we 
assume  that  the  time  interval  between  the  arrival  of  the  two 
pulses  at  the  ion  is  small  compared  with  the  free  time  of  vibration 
of  the  ion).  The  second  pulse  gives  to  the  ion  a  momentum  equal 
and  opposite  to  that  given  to  it  by  the  first  pulse  and  thus  reduces 
it  to  rest :  the  joint  action  of  the  two  pulses  is  thus  to  leave  the 


272  IONISATION   BY   RONTGEN   RAYS.  [138 

velocity  of  the  ion  unaltered,  and  to  displace  the  ion  through  a 
distance  f  given  by  the  equation 

t_Xe  d  jD 
*  ~  m    F  F ' 

If  we  suppose  that  the  ion  was  in  equilibrium  in  the  position 
f  =  0,  and  that  when  displaced  from  this  position  the  force  tending 
to  bring  it  back  is  //,£,  the  work  done  in  displacing  the  ion 
through  the  distance  f  is  i/^f 2,  thus  the  energy  communicated  by 
the  positive  and  negative  pulses  to  the  ion  is 

d2  D2 

yz  YZ  ' 

If  E  is  the  energy  in  the  two  pulses  per  unit  area,  we  have 

E  =  --~. 

Thus  the  work  done  on  the  ion  is  equal  to 

e2  dD2  r 


If  n  is  the  frequency  of  the  free  vibration  of  the  ion,  nz  =  p/m,  so 
that  the  work  done  on  the  ion  is 


a  „ 

-mi*    -   T-=-  E 
m   F2 

e2  dDz  „ 


where  \  is  the  wave-length  of  the  free  vibration  of  the  ion.  Thus 
the  work  done  on  the  ions  when  the  two  pulses  travel  over  a 
distance  Sx,  is  equal  to 

4-7T3  -  d.D*2^  EZx  =  hESa;,  say, 
Tit  AT 

where  N  is  the  number  of  ions  giving  out  light  of  the  wave-length 
X  in  unit  volume,  hence  we  have 

dE---hE 

J  "~~  ti/JJ/f 

dx 

or  E  =  E0e~hx  ; 

h  is  thus  the  coefficient  of  absorption  of  the  medium  for  the 
Rontgen  rays  :  when  we  take  into  account  the  energy  absorbed  by 


138]  1ONISATION   BY   RONTGEN   RAYS.  273 

the  ions  and  neglect  that  radiated  by  them,  we  see  that  h  increases 
with  the  thickness  of  each  pulse  and  the  distance  between  the 
pulses,  it  thus  depends  upon  the  character  of  the  primary  rays ; 
the  broader  the  pulses  the  greater  the  absorption.  Thus  on  this 
view  of  the  nature  of  the  Rontgen  rays  the  soft  rays  correspond  to 
broad  pulses,  the  hard  rays  to  narrow  ones. 

Sagnac,  by  allowing  secondary  rays  to  fall  on  metal,  has  ob- 
tained tertiary  rays,  which  are  even  more  easily  absorbed  than  the 
secondary;  he  suggests  that  by  a  repetition  of  this  process  we 
might  ultimately  get  rays  having  the  properties  of  ordinary 
light.  As  yet  however  no  Rontgen  rays  have  been  obtained  which 
show  any  trace  of  refraction  when  passing  from  one  medium  to 
another. 


T.  G.  18 


CHAPTER  XII. 

BECQUEREL  RAYS. 

139.  THE  very  marked  phosphorescence  produced  in  certain 
substances  by  Rb'ntgen  rays  led  to  a  series  of  investigations  whose 
object  was  to  see  whether  phosphorescence  was  accompanied  by 
the  emission  of  Rontgen  rays:  since  Rontgen  rays  produced 
phosphorescence  the  question  naturally  suggested  itself,  may  not 
phosphorescence  be  accompanied  by  Rontgen  rays  ?  Early  in  1896 
Henry*  showed  that  the  phosphorescent  substance  sulphide  of  zinc, 
after  exposure  to  sunlight  or  magnesium  light,  acted  photographi- 
cally on  a  plate  protected  by  black  paper  or  by  thin  aluminium 
foil.  A  little  later  Becquerelf  found  that  if  the  double  sulphate 
of  uranium  and  potassium  was  placed  on  a  photographic  plate 
protected  by  light-proof  paper  and  the  system  exposed  to  the 
sun  the  plate  was  affected :  he  thought  at  first  that  this  was  due 
to  the  phosphorescence  emitted  by  the  uranium  while  in  the 
light,  he  soon  found  however  that  exposure  to  the  sunlight  was 
not  necessary {,.  and  that  the  plate  was  equally  affected  in  the 
dark.  To  test  whether  this  effect  was  due  to  a  phosphorescence 
which  had  persisted  from  some  previous  exposure  of  the  uranium 
salt  to  light  §  he  took  a  crystal  of  uranium  nitrate  and  dissolved 
it  in  water  in  the  dark;  he  then,  keeping  it  still  in  the  dark, 
allowed  it  to  recrystallise,  and  tested  its  action  on  the  photo- 
graphic plate  without  ever  exposing  the  crystal  to  light ;  he  found 
that  it  acted  strongly  on  the  plate;  he  found  also  that  the  solu- 
tion of  uranium  nitrate  which  is  not  phosphorescent  is  active. 
On  these,  grounds  Becquerel  came  to  the  conclusion  that  the 

*  Henry,  Comptes  Eendus,  cxxii.  p.  312,  1896. 
t  Becquerel,  Comptes  Rendus,  cxxii.  p.  420,  1896. 
J  Ibid.  p.  501. 
§  Ibid.  pp.  691,  765. 


140] 


BECQUEREL  RAYS. 


275 


effect  is  not  due  to  phosphorescence  but  is  a  property  of  the 
metal  itself.  He  found  too  that  the  salts  of  uranium  as  well  as 
the  metal  itself  retained  this  radio-active  property  without  sensible 
diminution  after  being  kept  in  the  dark,  some  of  them  in  lead 
boxes,  for  more  than  a  year.  In  addition  to  affecting  a  photo- 
graphic plate  protected  by  a  covering  opaque  to  ordinary  light, 
the  radiation  from  uranium,  like  the  Rontgen  rays,  makes  the  gas 
through  which  it  passes  a  conductor ;  thus  a  charged  electroscope 
with  a  piece  of  uranium  placed  on  the  disc  slowly  loses  its  charge, 
whether  this  be  positive  or  negative.  Becquerel  at  first  thought 
that  the  rays  from  uranium  differed  from  the  Rontgen  rays  in 
being  capable  of  refraction  and  polarisation ;  subsequent  investiga- 
tions made  by  himself  and  others  have  shown  however  that  this 
is  not  the  case. 

140.  Rutherford*  made  a  very  extensive  series  of  experiments 
on  the  radiation  from  uranium  and  its  compounds,  using  the  elec- 
trical method  of  investigation,  i.e.  measuring  the  intensity  of  the 
radiation  by  the  ionisation  produced  by  the  rays.  He  made  the 
very  interesting  discovery  that  the  radiation  from  uranium,  like 
the  secondary  Rontgen  radiation,  is  a  mixture  of  two  types  of 
radiation,  one  type  a  being  absorbed  by  a  few  millimetres  of  air 
at  atmospheric  pressure,  the  other  type  ft  having  a  penetrating 
power  comparable  with  the  rays  from  a  Rontgen  tube  of  moderate 
exhaustion.  This  fact  is  illustrated  by  the  following  table,  which 
shows  the  effect  of  successive  layers  of  very  thin  aluminium  foil 
in  cutting  down  the  intensity  of  the  radiation. 

Thickness  of  aluminium  foil,  '0005  cm. 


Number  of  layers  of 
Aluminium  foil 

Leak  per  minute  in. 
scale  divisions 

Proportion  in  which  the 
diminished  by  one  layer 

leak  is 
of  foil 

0 

182 

1 

77 

•42 

2 

33 

•43 

3 

14-6 

•44 

4 

9-4 

•65 

12 

7 

From  these  numbers  we  see  that  the  first  layer  of  aluminium 
foil  cuts  down  the  intensity  of  the  radiation  to  about  one-half  of 

*  Rutherford,  Phil.  Mag.  v.  47,  p.  109,  1899. 

18—2 


276  BECQUEREL   RAYS.  [140 

its  original  value,  the  second  and  third  layers  each  diminish  it  in 
much  the  same  proportion,  the  fourth  layer  however  produces 
sensibly  less  effect,  while  the  joint  effect  of  the  next  eight  layers 
is  small ;  in  fact  to  reduce  the  intensity  of  the  radiation  to  one- 
half  the  value  it  has  after  passing  through  four  layers  of  foil 
requires  the  interposition  of  one  hundred  additional  layers.  Thus 
before  the  rays  had  been  filtered  by  the  foil,  one  layer  of  foil 
produces  as  much  absorption  as  one  hundred  layers  after  the 
filtering  has  taken  place.  These  results  show  that  part  of  the 
radiation  emitted  from  the  uranium  is  almost  entirely  absorbed 
by  about  four  layers  of  foil,  while  there  is  another  part  of  very 
much  greater  penetrating  power  which  can  pass  through  about 
one  hundred  layers  of  foil  before  its  intensity  is  reduced  to  one- 
half.  Rutherford  calls  the  easily  absorbable  radiation  the  a 
radiation,  the  other  the  /3  radiation.  The  penetrating  power  of 
the  /3  radiation  is  of  the  same  order  as  that  of  Rontgen  rays 
emitted  by  an  average  bulb.  Rutherford  found  that  the  absorption 
by  the  different  gases  of  the  a  type  of  radiation  emitted  by 
uranium  or  any  of  its  compounds  was  such  that  the  intensity  of 
the  radiation  was  reduced  to  one-half  its  value  after  passing 
through 

3  mm.  of  carbonic  acid  gas, 

4' 3  mm.  of  air, 

7 '5  mm.  of  coal  gas, 

16*3  mm.  of  hydrogen. 

The  pressure  in  all  cases  was  that  due  to  760  mm.  of  mercury. 
The  penetrating  power  of  the  a  radiation  is  thus  intermediate 
between  that  of  ordinary  primary  and  secondary  Rontgen  rays. 

The  absorption  of  the  a  rays  was  shown  by  Rutherford  to  be 
proportional  to  the  density  of  the  gas. 

Near  a  layer  of  uranium  we  have  thus  a  region  of  very  intense 
ionisation  extending  over  the  few  millimetres  necessary  to  absorb 
all  the  a  rays,  beyond  this  only  the  ft  rays  penetrate,  and  as  these 
have  only  small  ionising  power  compared  with  the  a  rays  there  is 
'in  this  region  very  much  less  ionisation  than  in  the  layers  close  to 
the  uranium.  Thus  if  we  have  two  parallel  metal  plates  over  one 
of  which  a  layer  of  uranium  is  spread,  then  if  the  distance 
between  the  plates  is  greater  than  that  required  to  absorb  the  a 
radiation,  the  total  amount  of  ionisation  between  the  plates  and 


140] 


BECQUEREL   RAYS. 


277 


therefore  the  value  of  the  saturation  current  which  can  pass  from 
one  plate  to  the  other  will  not  increase  much  as  the  distance 
between  the  plates  is  increased,  while  as  long  as  the  distance 
between  the  plates  is  less  than  that  required  to  absorb  the  a 
radiation  the  saturation  current  will  be  approximately  propor- 
tional to  the  distance  between  the  plates ;  this  illustration  will 
suffice  to  show  that  the  phenomena  of  electric  conduction  under 
uranium  radiation  are  somewhat  intricate,  they  can  however  be 
readily  explained  by  the  existence  of  the  two  types  of  radiation, 
one  very  easily  absorbed,  the  other  much  more  penetrating. 

Since  the  intensity  of  the  ionisation  is  much  greater  close  to 
the  plate  covered  with  uranium  than  at  some  distance  away,  the 
electric  force  near  to  the  uranium  will  be  less  than  the  average 
value  between  the  plates ;  this  fall  in  the  electric  force  at  the 
place  where  there  is  most  ionisation  makes  it  more  difficult  to 
produce  a  saturation  current  than  it  would  be  if  the  ionisation 


I 


Cy 


•375 


cms 


40 


80 


160 


200 


Fig.  74. 


were  uniform  between  the  plates ;  this  may  account  for  the  fact 
discovered  by  Rutherford  (I.  c.)  that  even  with  large  potential 
differences  between  the  plates  the  current  shows  an  increase, 


278 


BECQUEREL   RAYS. 


[141 


though  only  a  small  one,  when  the  potential  difference  is  in- 
creased. This  is  illustrated  in  the  curves  in  Fig.  74  which 
represent  the  relation  between  the  potential  difference  and  the 
current  under  uranium  radiation. 

The  proportion  between  the  amounts  of  the  ft  and  a  radiations 
emitted  by  a  layer  of  a  salt  of  uranium  was  found  by  Rutherford 
(I.  c.)  to  depend  upon  the  thickness  of  the  layer  of  salt,  the  thicker 
the  layer  the  larger  the  ratio  of  the  ft  to  the  a.  radiation.  This  is 
what  we  should  expect  if  we  regard  the  a  and  ft  radiations  as 
independent  of  each  other :  for  if  the  a  radiation  is  stopped  by  a 
thickness  t-^  of  the  salt,  while  the  ft  radiation  is  not  stopped  until 
the  thickness  is  t2,  the  a  radiation  will  not  increase  with  the 
thickness  of  the  layer  when  this  is  greater  than  tl}  while  the  ft 
radiation  will  go  on  increasing  until  the  thickness  is  equal  to  t2. 
If  one  of  the  radiations  was  produced  by  the  other,  if  for  example 
the  ft  radiation  corresponded  to  primary  Rontgen  rays,  the  a  to 
the  more  absorbable  secondary  rays  produced  by  the  impact  of  the 
primary  ones  with  the  uranium  close  to  the  surface,  then  we  should 
expect  the  proportion  between  the  radiations  to  be  independent  of 
the  thickness  of  the  layer. 

141.  lonisation  in  different  gases.  Since  the  a  radiation  is 
absorbed  by  a  few  millimetres  of  most  gases,  the  total  amount  of 
ionisation  produced  on  different  gases  when  it  is  completely  ab- 
sorbed can  be  readily  determined :  the  result  of  such  a  determina- 
tion made  by  Rutherford  (I.  c.)  is  given  in  the  following  table. 


Gas 

Total  lonisation 

Gas 

Total  lonisation 

Air  

100 

111 

Hydrogen 

95 

Hydrochloric  ) 

Oxygen 

106 

acid  gas  j   ' 

102 

Carbonic  acid 

96 

Ammonia   

101 

The  salt  used  to  produce  the  rays  was  uranium  oxide,  and  as 
its  radiating  power  was  slightly  affected  by  ammonia  and  hydro- 
chloric acid  the  numbers  for  these  gases  must  be  regarded  as  only 
approximately  true.  It  will  be  seen  that  the  numbers  expressing 
the  total  ionisation  produced  in  the  various  gases  when  all  the 
radiation  is  absorbed  are  very  nearly  equal ;  so  nearly  indeed  that 


141]  BECQUEREL   RAYS.  279 

we  cannot  say  with  certainty  that  the  differences  are  not  due 
to  experimental  errors.  The  experiments  thus  point  very  dis- 
tinctly to  the  conclusion  that  the  absorption  of  a  fixed  quantity 
of  Becquerel  rays  gives  rise  to  the  same  number  of  ions  whatever 
may  be  the  nature  of  the  gas  ionised;  we  saw  (p.  251)  that  Ruther- 
ford's experiments  on  the  absorption  of  Rontgen  rays  indicated 
that  a  similar  result  was  true  for  these  rays.  We  may  express 
this  result  in  the  form  that  when  all  the  rays  whether  Becquerel 
or  Rontgen  are  absorbed  in  a  certain  volume  of  gas,  the  maximum 
quantity  of  electricity  which  can  be  forced  through  the  gas 
depends  only  upon  the  intensity  of  the  rays  and  not  upon  either 
the  composition  or  pressure  of  the  gas.  This  result  is  so  in- 
teresting that  it  is  worth  while  discussing  it  a  little  more  closely. 
The  energy  absorbed  may  be  spent  (1)  in  ionising  the  gas,  (2)  in 
raising  the  temperature  of  the  gas.  Suppose  that  the  rays  are 
travelling  parallel  to  the  axis  of  x,  let  /  be  the  intensity  of  the 
rays  at  the  distance  x  from  the  origin,  7  +  S7  the  intensity  at 
x  +  Sx ;  —  SI  is  the  energy  absorbed  in  the  layer  S%. 

Suppose  that  the  number  of  ions  produced  is  proportional  to 
the  energy  of  the  rays,  and  that  the  number  produced  in  the  layer 
$x  is  equal  to  X7S#,  let  the  work  required  to  produce  an  ion  be  a, 
then  the  energy  absorbed  in  ionising  the  gas  is  aXl&x;  let  the 
amount  absorbed  as  heat  *  in  the  layer  be  ql&x,  then  we  have 

_  SI  =  (q  +  «X)  IBx  or  1=  Ce~  <2+aA>  * 
where  C  is  the  value  of  7  when  x  =  0. 

The  number  of  ions  produced  when  the  radiation  is  all  absorbed 
is  equal  to 

roo  -so 

\Idx  =       C\e~ 


/• 

= 
J 


o 

Rutherford's  experiments  show  that  as  long  as  C  is  constant  this 
number  is  independent  of  the  nature  of  the  gas;  this  shows  that 
the  production  of  each  pair  of  positive  and  negative  ions  abstracts 
from  the  energy  of  the  rays  an  amount  of  energy  which  is  inde- 
pendent of  the  nature  of  the  gas  ionised  :  if  all  the  energy 
absorbed  were  spent  in  ionising  the  gas  this  result  would  imply 
that  the  energy  required  to  produce  a  given  number  of  ions  was 

*  If  the  ions  are  allowed  to  recombine  all  the  energy  will  ultimately  appear 
as  heat. 


280  BECQUEREL  RAYS.  [141 

independent  of  the  nature  of  the  gas  from  which  the  ions  are 
obtained.  The  evidence  seems  however  to  be  against  the  view 
that  the  separation  of  ions  from  the  molecules  of  the  gas  is  the 
only  source  by  which  the  rays  lose  energy.  Rutherford  and 
McClung*  have  measured  the  energy  in  Rontgen  rays,  and  also 
the  total  amount  of  ionisatioii  these  rays  would  produce  if  they 
were  completely  absorbed  by  a  gas.  The  energy  in  the  rays  was 
measured  by  absorbing  them  in  thin  strips  of  platinum  used  in  a 
bolometer  and  determining  the  heating  effect  from  the  change  in 
resistance.  Dornf  had  previously  shown  that  appreciable  thermal 
effects  were  produced  by  the  absorption  of  Rontgen  rays  in  thin 
sheets  of  metal,  and  had  by  this  means  measured  the  energy  in 
the  rays.  Measurements  of  this  kind  give  us  C,  while  the  measure- 
ment of  the  total  number  of  ions  gives  us  C\/(q  +  «X),  combining 
the  two  we  get  (q  +  «X)/X.  Rutherford  and  McClung  assumed 
that  the  energy  of  the  Rontgen  rays  was  entirely  spent  in  ionising 
the  gas,  so  that  if  the  ions  were  prevented  from  recombining  by 
means  of  a  strong  electric  field  no  heat  was  developed  in  the  gas  ; 
on  this  supposition  q  =  0,  so  that  (q  +  aX)/X  is  equal  to  a,  the  work 
required  to  produce  an  ion.  Making  this  supposition  Rutherford 
and  McClung  found  that  the  work  required  to  ionise  a  gas  was 
equivalent  to  the  work  done  when  each  ion  was  moved  through  a 
potential  difference  of  about  95  volts,  so  that  since  the  ions  are 
produced  in  pairs  it  would  require  a  potential  difference  of  at 
least  190  volts  to  separate  the  ions.  We  saw  however  (p.  190) 
that  the  experiments  made  by  H.  A.  Wilson  on  the  ionisation  of 
hot  gases  indicated  that  a  much  smaller  difference  of  potential— 
about  2  volts  —  is  all  that  is  required  to  ionise  a  gas,  this  conclusion 
is  confirmed  by  other  lines  of  argument.  If  we  take  Wilson's 
value  for  the  work  required  to  ionise  a  gas,  we  see  that  a  is  the 
work  done  when  the  ionic  charge  is  moved  through  the  potential 
difference  of  about  1  volt.  Rutherford's  and  McClung's  experi- 
ments show  that  in  the  case  of  the  Rontgen  rays  used  by  them 

a  +     =  95a, 


or 


*  Rutherford  and  McClung,  Phil.  Trans.  A.  cxcvi.  p.  25,  1902. 
t  Dorn,  Wied.  Ann.  Ixiii.  p.  160,  1897. 


142]  BECQUEREL   RAYS.  281 

Thus  for  each  ion  produced  the  mechanical  equivalent  of  the 
heat  developed  in  the  gas  is  about  94  times  the  work  required  to 
separate  the  ion  from  the  molecule. 

Rutherford's  experiments  on  the  ionisation  produced  by  the 
complete  absorption  of  the  a  radiation  from  uranium  show  that 
if  the  number  of  ions  produced  is  proportional  to  the  energy  in 
the  rays,  then  as  long  as  the  rays  remain  the  same  the  liberation 
of  an  ion  always  abstracts  the  same  amount  of  energy  from  the 
rays  whatever  may  be  the  nature  of  the  gas.  This,  since  by  far 
the  greater  part  of  the  absorption  of  energy  is  apparently  due  to 
the  heating  of  the  gas,  is  a  very  remarkable  result.  We  do  not 
know  however  whether  or  not  the  amount  of  energy  absorbed 
when  an  ion  is  produced  depends  upon  the  nature  of  the  rays, 
whether  for  example  it  is  the  same  for  Becquerel  as  for  Rontgen 
rays,  for  hard  Rontgen  rays  as  for  soft.  It  is  much  to  be  desired 
that  experiments  of  the  type  of  those  made  by  Rutherford  and 
McClung  should  be  made  with  as  many  kinds  of  rays  as  possible. 

If  we  regard  the  Rontgen  and  Becquerel  rays  as  pulses  of 
electric  and  magnetic  force  made  up  of  Faraday  tubes,  we  may 
see  why  the  amount  of  ionisation  should  not  depend  upon  the 
nature  of  the  gas :  for  when  a  pair  of  ions  is  separated  the  ends 
of  one  of  the  Faraday  tubes  in  the  pulse  will  now  be  on  the  ions, 
one  end  on  the  positive,  the  other  end  on  the  negative  ion ;  this 
Faraday  tube  gets  anchored  as  it  were  by  the  ions,  and  is  dragged 
back  from  the  pulse  which  passes  on  without  it.  Thus  each  pair 
of  ions  means  the  abstraction  of  one  Faraday  tube  from  the  pulse, 
and  when  all  the  tubes  are  extracted,  the  number  of  ions  produced 
will  be  twice  the  number  of  Faraday  tubes  originally  in  the  pulse 
and  independent  of  the  nature  of  the  gas. 

142.  The  total  amount  of  ionisation  produced  when  the 
a  rays  of  uranium  and  its  salts  are  completely  absorbed  has  be  n 
determined  by  Monsieur  and  Madame  Curie*  and  by  Rutherford 
and  McClungf,  it  increases  somewhat  with  the  thickness  of  the 
layer,  as  the  following  table  given  by  the  latter  observers  shows. 
The  amount  of  ionisation  is  expressed  in  terms  of  the  saturation 
current  which  is  given  in  amperes  per  square  centimetre  of 
surface. 

*  Curie,  Rapports  presentes  au  Congres  de  Physique  a  Paris,  t.  iii.  p.  79,  1900. 
t  Rutherford  and  M'Clung,  Phil.  Trans.  A.  cxcvi.  p.  25. 


282  BECQUEREL   RAYS.  [143 

Surface  of  Uranium  Oxide  =  38  sq.  cms. 


Weight  of  Uranium  Oxide  spread 
over  this  surface  in  grammes 


•138 
•365 
•718 
1-33 
3-63 


Current  in  Amperes  per 
sq.  cm.  of  surface 


17  xlO-13 
3-2xlO~13 
4  xlO'13 
4-4  xlO~13 
4-7  xlO-13 


Taking  the  value  given  by  Rutherford  and  McClung  for  the 
energy  .absorbed  when  each  ion  is  produced,  we  find  that  when 
the  saturation  current  is  4*7  x  10~13  amperes  per  square  centimetre 
the  energy  emitted  from  a  square  centimetre  is  about  10~n  calories 
per  second,  or  at  the  rate  of  1  calorie  in  about  3000  years.  If  we 
take  the  radiation  corresponding  to  the  thinnest  layer  we  find 
that  for  each  gramme  in  the  layer  it  is  about  1  calorie  in  30  years. 

Magnetic  Deflection  of  the  more  penetrating  Uranium  Rays. 

143.  The  fact  that  some  of  the  rays  given  out  by  some  radio- 
active substances  are  deflected  by  a  magnet  was  first  discovered  for 
the  radiation  from  radium,  we  shall  give  an  account  of  these  experi- 
ments when  we  discuss  the  radiation  from  that  body.  Becquerel* 
subsequently  found  that  the  /3  rays  from  uranium  were  deflected 
by  a  magnet,  the  direction  of  the  deflection  being  the  same  as 
that  of  the  cathode  rays  :  so  that  for  this  arid  other  reasons  we 
conclude  that  the  ft  rays  consist  of  negatively  charged  particles. 
Assuming  that  the  ratio  of  the  mass  to  the  charge  for  the  ft  rays 
is  the  same  as  for  the  cathode  rays,  Becquerel  from  his  determina- 
tion of  the  magnetic  deflection  of  these  rays  concluded  that  they 
were  moving  with  a  velocity  of  2  x  1010  cm.  per  sec.:  this  velocity, 
which  is  two-thirds  of  that  of  light,  is  considerably  greater  than 
that  of  any  cathode  rays  hitherto  produced  by  electrical  means. 

The  a  rays  from  radium,  have  been  shown  by  Rutherford  •(•  to 
carry  a  positive  charge,  and  Becquerel {  has  shown  that  they  are 
deflected  by  a  strong  magnetic  field  in  the  direction  corresponding 
to  a  charge  of  this  sign. 

*  Becquerel,  Comptes  Rendus,  cxxx.  p.  1583 ;  cxxxi.  p.  137,  1900. 

t  Rutherford,  Phil.  Mag.  vi.  5,  p.  177,  1903. 

£  Becquerel,  Comptes  Rendus,  cxxxvi.  p.  431,  1903. 


144]  BECQUEREL  RAYS.  283 

144.  Sir  William  Crookes*  concludes  that  the  radiation  from 
uranium  does  not  proceed  from  uranium  itself,  but  from  some 
unknown  impurity.  The  reason  for  this  conclusion  is  that  by  a 
process  of  fractionation  he  has  obtained,  starting  from  uranium  salts, 
two  products,  one  of  which  is  radio-active,  while  the  other  is  not. 

One  of  these  processes  consists  in  dissolving  crystallised  uranium 
nitrate  in  ether,  the  uranium  divides  itself  unequally  between  the 
ether  and  the  water  present,  the  larger  part  which  is  in  the  ether 
layer  does  not  affect  a  photographic  plate,  while  the  smaller 
portion  which  is  in  the  water  layer  possesses  all  the  photographic 
activity  of  the  original  nitrate.  Soddyf*,  who  repeated  this 
experiment  using  "for  the  radio-activity  the  electrical  test,  i.e.  the 
amount  of  ionisation  produced,  'found  that  both  portions  were 
equally  active,  so  that  apparently  no  separation  had  been  effected. 
The  explanation  of  this  discrepancy  is  that  in  the  photographic 
method  the  rays  have  to  pass  through  glass  or'  card  before 
reaching  the  film,  so  that  all  the  absorbable  a  rays  are  stopped 
and  only  the  ft  rays  are  detected :  in  the  electrical  method  however 
the  ionisation  is  practically -entirely  produced  by  the  a  radiation, 
thus  the.  photographic  method  detects  the  ft,  the  electrical  method 
the  a  radiation,  so  that  the  experiments  show  the  separation 
is  confined  to  the  substance  producing  the  ft  radiation.  Another 
process  employed  by  Crookes  to  separate  the  active  consti- 
tuent— UrX — from  the  other  consisted  in  precipitating  solutions 
of  uranium  nitrate  with  ammonium  carbonate  in  excess,  the  small 
amount  of  precipitate  was  collected  •  an.d  the  filtrate  evaporated, 
another  and  much  larger  precipitate  came  down;  the  first  of 
these  precipitates  strongly  affected  a  photographic  plate,  while 
the  second  was  almost  inactive.  On  testing  these  by  the  elec- 
trical method  Soddy  found  that  the  second  precipitate  produced 
a  considerable  ionisation,  while  the  effect  of  the  small  quantity 
of  the  first  was  barely  perceptible ;  the  explanation  of  this  is  the 
same  as  before,  and  Rutherford  and  GrierJ  have  shown  by  direct 
experiment  that  the  first  precipitate  emits  nothing  but  the 
cathodic-magnetically  deflectable  ft  radiation,  while  the  second 
precipitate  emits  nothing  but  the  a  radiation. 

*  Crookes,  Proc.  Roy.  Soc.  Ixvi.  p.  409,  1900. 

t  Soddy,  Ghent.  Soc.  Journ.  Ixxxi.,  Ixxxii.  p.  860,  1902. 

t  Rutherford  and  Grier,  Phil.  Mag.  vi.  4,  p.  315,  1902. 


284 


BECQUEREL   RAYS. 


[145 


145.  Becquerel*  made  the  very  interesting  observation  that 
when  he  had  enfeebled  the  radio-activity  of  uranium  by  precipi- 
tating barium  as  sulphate  from  uranium  solutions  and  transferred 
most  of  the  (/3)  activity  to  the  barium,  on  allowing  the  products  to 
stand  for  several  months  the  enfeebled  uranium  had  recovered  its 
normal  activity,  while  the  barium  which  had  been  made  radio- 
active had  entirely  lost  this  property ;  a  similar  phenomenon  was 
discovered  by  Rutherford  and  Soddy  in  the  case  of  thorium,  and 
their  investigations  on  this  point  led  to  very  important  considera- 
tions as  to  the  production  of  radio-activity;  these  are  discussed 
on  p.  292. 

Radiation  from  Thorium. 

146.  Soon  after  the  discovery  of  the  Becquerel  rays  Schmidt  J- 
discovered    that   thorium    gave    out    rays   having   very   similar 
properties.     This  radiation  was  subsequently  studied  by  Ruther- 
ford J  and  by  Owens§,  and  was  found  to  present  many  features  of 
great  interest. 

When  a  thin  layer  of  thorium  oxide  is  used  the  radiation  is 
approximately  homogeneous,  as  the  following  results  given  by 
Rutherford  show :  successive  layers  of  thin  paper  were  placed 
over  a  thin  layer  of  thorium  oxide,  and  the  intensity  of  radiation 
determined  by  measuring  the  rate  of  discharge  through  a  volume 
of  gas  sufficient  to  absorb  the  radiation  completely. 

Thickness  of  paper  =  -0027  cm. 


Number  of  layers  of  thin  paper 

Rate  of  Discharge 

0 

1 

1 

•37 

2 

•16 

3 

•08 

The  intensity  of  the  radiation,  which  is  proportional  to  the 
rate  of  discharge,  thus  diminishes  in  approximately  geometrical  pro- 
gression with  the  addition  of  equal  thicknesses  of  paper,  this  shows 

*  Becquerel,  Comptes  Rendus,  cxxxiii.  p.  977,  1901. 
t  Schmidt,  Wied.  Ann.  Ixv.  p.  141,  1898. 
J  Rutherford,  Phil.  Mag.  v.  49,  pp.  1,  161,  1900. 
§  Owens,  Phil.  Mag.  \.  48,  p.  360,  1899. 


147] 


BECQUEREL   RAYS. 


285 


that  the  radiation  is  roughly  homogeneous.  When  however  a  thick 
layer  of  the  oxide  is  used  there  is  in  addition  to  the  radiation  of 
the  type  given  out  by  the  thin  layer  other  radiation  of  a  much 
more  penetrating  type ;  this  is  proved  by  the  following  results, 
which  were  also  given  by  Rutherford. 

Thick  layer  of  oxide. 
Thickness  of  paper  =  '008  cm. 


Number  of  layers  of  paper 

Bate  of  Discharge 

0 

1 

1 

•74 

2 

•74 

5 

•72 

10 

•67 

20 

•55 

Thus  the  first  layer  of  paper  produces  an  appreciable  diminu- 
tion in  the  intensity  of  the  radiation  due  to  the  absorption  of 
the  radiation  of  the  type  given  out  by  the  thin  layer,  but  after 
this  is  absorbed  there  is  an  appreciable  amount  of  radiation  left 
which  can  pass  through  a  considerable  thickness  of  paper  without 
suffering  much  absorption. 

147.  The  radiation  from  thick  layers  of  thorium  oxide  when  first 
measured  by  Rutherford  seemed  to  be  extremely  capricious  ;  thus, 
for  example,  when  its  intensity  was  measured  by  the  conductivity  it 
communicated  to  a  gas,  the  slightest  draught  in  the  vessel  through 
which  the  current  of  electricity  passed  was  sufficient  to  produce 
a  very  sensible  diminution  in  the  current ;  indeed  so  sensitive  was 
the  current  to  external  disturbances,  that  it  was  found  exceedingly 
difficult  to  get  consistent  results.  Rutherford  showed  that  those 
irregularities  had  a  most  interesting  cause,  as  he  was  able  to  trace 
them  to  an  '  emanation '  given  off  by  the  thorium.  He  found 
that  the  thorium  gave  off  something  which  was  wafted  about  by 
currents  of  air  like  a  vapour;  in  order  to  avoid  prejudging  the 
question  as  to  the  physical  state  in  which  the  substance  given 
off  by  the  thorium  existed,  Rutherford  called  it  an  emanation. 
This  emanation  is  radio-active,  i.e.  it  gives  off  rays  that  can 
penetrate  a  photographic  plate  or  ionise  a  gas ;  it  can  penetrate, 
apparently  by  diffusion,  thin  sheets  of  metal  or  pieces  of  paper ; 


286  BECQUEREL   RAYS.  [147 

it  cannot,  however,  get  through  glass  or  mica,  even  when  they  are 
in  very  thin  films :  in  fact,  its  power  of  getting  through  substances 
seems  much  more  selective  than  the  corresponding  power  possessed 
by  either  Rontgen,  Becquerel,  or  cathode  rays ;  in  this  respect  it 
resembles  the  effect  coming  from  certain  metals  and  resinous 
substances  studied  by  Russell.  That  the  passage  of  the  emanation 
through  solids  is  analogous  to  the  slow  diffusion  of  gas  through 
metal,  as,  for  example,  hydrogen  through  red-hot  platinum,  is 
suggested  by  the  fact  that  if  the  thorium  oxide  is  covered  up 
with  paper  it  takes  a  considerable  time  for  the  emanation  to 
get  through. 

The  following  experiment  is  one  by  which  Rutherford  demon- 
strated the  existence  of  the  '  emanation,'  and  studied  many  of 
its  properties. 

A  thick  layer  of  thorium  oxide  was  enclosed  in  a  narrow 
rectangular  vessel  A,  made  up  of  two  thicknesses  of  foolscap 
paper.  This  paper  was  sufficiently  thick  to  stop  all  the  radiation 
from  a  thin  layer  of  thorium.  The  vessel  containing  the  thorium 


Fig.  75. 

was  placed  inside  a  long  metal  tube  B.  One  end  of  this  tube 
was  connected  with  a  large  insulated  vessel  C,  the  end  of  this 
vessel  was  perforated  to  allow  air  to  pass  through.  An  insulated 
electrode  D  was  inserted  in  G,  and  connected  with  one  pair  of 
quadrants  of  an  electrometer.  C  was  connected  with  one  terminal 
of  a  battery  giving  an  electromotive  force  of  100  volts,  the  other 
terminal  of  this  battery  was  put  to  earth. 

A  slow  current  of  dust-free  air  was  passed  through  the  appa- 
ratus. After  a  short  time  a  current  began  to  pass  between  C 
and  D,  and  gradually  increased  until  it  reached  a  certain  value, 
when  it  became  steady.  The  flow  of  air  was  then  stopped,  and 


147]  BECQUEREL  RAYS.  287 

it  was  found  that  the  current  between  0  and  D  persisted  for 
about  10  minutes.  As  long  as  the  current  of  air  was  passing 
through  the  apparatus  there  would  have  been  a  current  of  elec- 
tricity between  C  and  D,  if  ordinary  radiation  and  no  emanation 
had  been  coming  from  the  thorium,  for  the  radiation  would  have 
produced  ionised  gas  in  the  neighbourhood  of  A,  and  this  would 
have  been  carried  by  the  current  into  C:  but  in  this  case  the  current 
of  electricity  would  have  stopped  within  a  fraction  of  a  second 
after  the  stoppage  of  the  current  of  air,  whereas,  as  we  have  seen, 
the  effect  persisted  for  10  minutes.  This  shows  that  fresh  ions 
must  be  continually  produced  in  (7,  in  other  words,  the  substance 
carried  over  from  A  must  be  radio-active,  and  though  its  radio- 
activity diminishes  with  time  there  is  enough  left  to  be  appreci- 
able after  an  interval  of  10  minutes. 

Rutherford  measured   the  leak  between  G  and  D  at  regular 

o 

intervals  after  the  stoppage  of  the  current  of  air,  and  so  was 
able  to  measure  the  rate  at  which  the  intensity  of  the  radiation 
from  the  emanation  died  away:  the  intensity  diminishes  in 
geometrical  progression  with  the  time,  and  is  thus  proportional 
to  e~A^,  where  t  is  the  time  and  X  a  constant :  the  intensity  is 
reduced  to  about  one-half  its  value  in  one  minute,  so  that  \  is 
about  1/86.  The  rate  at  which  the  radiation  falls  off  is  not 
affected  by  exposing  the  emanation  to  a  strong  electric  field,  nor 
could  any  motion  of  the  emanation  as  a  whole  be  detected  in 
such  a  field :  Rutherford  showed  that  the  average  velocity  of  the 
particles  of  the  emanation,  under  an  electric  field  of  one  volt  per 
centimetre,  must  be  less  than  10~6  cm./sec. 

In  consequence  of  the  diffusion  of  the  emanation  from  the 
thorium  the  radiation  from  thick  layers  of  this  substance  does 
not  cast  shadows,  the  emanation  getting  by  diffusion  round  the 
opaque  body  and  obliterating  the  shadow. 

The  emanation  can  pass  through  plugs  of  porous  substances, 
can  bubble  through  water  or  the  strongest  acids,  and  can  be 
raised  to  temperatures  far  above  a  red-heat  without  losing  its 
radio-activity  * :  in  fact,  when  once  the  '  emanation '  has  been 
produced  no  physical  or  chemical  process  which  has  yet  been 
tried  has  any  effect  upon  its  radio-activity:  in  this  inertness  it 

*  Rutherford  and  Soddy,  Journal  of  Chemical  Society,  Ixxxi.  p.  321,  1902. 


288  BECQUEREL   RAYS.  [148 

resembles  the  gases  argon  and  helium,  the  latter  of  which  occurs 
along  with  thorium  in  many  minerals. 

Since  the  emanation  can  penetrate  several  millimetres  of  a 
thorium  compound,  the  radiation  from  a  layer  of  such  a  compound 
will  increase  with  the  thickness  of  the  layer  when  this  is  less 
than  a  few  millimetres;  above  a  certain  thickness  the  radiation 
becomes  practically  constant. 

The  fact  that  the  '  emanation '  can  pass  through  porous  plugs 
and  water  traps,  and  can  withstand  temperatures  which  alter  the 
properties  of  thorium,  is  strong  evidence  that  the  emanation  is 
not  thorium  dust,  i.e.  not  small  particles  of  thorium  in  the  solid 
state ;  this  conclusion  is  strengthened  by  the  fact  that  the  ema- 
nation does  not  give  rise  to  a  cloud  when  the  air  through  which 
it  is  diffused  suffers  an  expansion  sufficient  to  produce  a  fog  in 
dusty  air. 

No  alteration  has  been  detected  in  the  pressure  of  an  ex- 
hausted bulb  when  the  emanation  is  allowed  to  diffuse  into  it, 
nor  does  this  intrusion  of  the  emanation  produce  apparently  any 
change  in  the  spectrum  given  out  by  the  bulb. 

Effect  of  Physical  Conditions  on  Emanating  Power. 

148.  Effect  of  Temperature.  This  has  been  investigated  by 
Rutherford*  and  by  Rutherford  and  Soddyf,  who  have  shown  that 
an  increase  of  temperature  up  to  a  certain  limit — about  a  red-heat — 
increases  the  emanating  power  of  thorium  oxide.  The  maximum 
reached  is  between  three  and  four  times  the  value  at  ordinary 
atmospheric  temperatures,  and  is  maintained  at  this  value  for 
several  hours  without  any  sign  of  diminution  with  time.  When 
the  thorium  is  allowed  to  cool  the  emanating  power  returns 
to  about  the  original  value.  When  the  thoria  is  heated  beyond 
a  certain  temperature  the  emanating  power  rapidly  falls  off  to 
a  fraction  of  its  former  value,  and  on  cooling  the  emanation  is 
found  to  be  small  compared  with  its  previous  value;  by  heating 
thoria  .to  the  highest  temperature  which  could  be  safely  employed 
with  platinum  vessels  and  then  allowing  it  to  cool,  the  emanating 
power  was  reduced  to  about  8  per  cent,  of  its  original  value. 

*  Rutherford,  Physikalische  Zeitschrift,  ii.  p.  429,  1901. 

t  Rutherford  and  Soddy,  Journal  of  Chemical  Soc.  Ixxxi.  p.  321,  1902. 


149]  BECQUEREL   RAYS.  289 

This  change  in  the  rate  of  emanation  is  accompanied  by  changes 
in  the  physical  and  chemical  properties  of  the  thoria ;  when  first 
the  de-emanation  sets  in  the  thoria  changes  in  colour  from  pure 
white  to  a  light  brown,  and  then  at  the  very  highest  tempera- 
tures to  a  pure  pink ;  and  at  the  same  time  the  solubility  of  the 
substance  in  sulphuric  acid  is  greatly  diminished.  Though  the 
emanation  is  so  greatly  diminished  by  this  intense  heating, 
the  radiation  from  thin  layers  of  the  substance — which,  following 
Rutherford,  we  shall  call  the  'straight  line'  radiation — is  not 
affected. 

Rutherford  and  Soddy  have  shown  that  the  loss  of  emanating 
power  of  thoria  can  be  remedied  by  chemical  treatment,  they 
found  that  if  the  de-emanated  thoria  was  dissolved  up  and  re- 
precipitated  it  recovered  completely  its  emanating  power. 

In  another  experiment  made  by  Rutherford  and  Soddy  the 
thoria  was  cooled  by  a  mixture  of  solid  carbonic  acid  and  ether, 
the  emanation  fell  to  about  10°/0  of  its  value  at  the  temperature 
of  the  room,  but  it  recovered  its  original  value  when  the  cooling 
agent  was  removed.  Thus  though  all  changes  of  temperature 
produce  marked  temporary  effects,  no  permanent  ones  are  pro- 
duced unless  the  temperature  exceeds  red-heat. 

149.  Effects  of  Moisture.  Dorn*  showed  that  the  emanation 
from  thoria  was  greater  in  a  moist  atmosphere  than  in  a  dry  one. 
Rutherford  and  Soddy  subsequently  confirmed  this,  and  found 
that  the  emanation  in  an  atmosphere  saturated  with  water 
vapour  was  about  20  °/0  greater  than  in  a  very  dry  atmosphere. 

There  are  many  phenomena  which  show  that  the  emanating 
power  of  a  thorium  compound  does  not  depend  merely  upon  the 
quantity  of  thorium  and  other  elements  in  the  material ;  the  way 
in  which  the  different  elements  are  combined  and  the  previous 
treatment  and  history  of  the  compound  have  a  great  influence 
upon  the  result.  Thus,  for  example,  the  emanating  power  of 
freshly  prepared  hydroxide  goes  on  increasing  for  some  time 
after  it  has  been  dried,  until  when  it  reaches  the  steady  state 
the  value  may  be  three  times  that  when  it  was  first  tested. 
This  seems  to  indicate  that  the  emanation  may  be  due  to  some 
compound  which  is  formed  but  slowly  :  the  effect  produced  by 

*  Dorn,  Abh.  der  Naturforsch.  Ges.fiir  Halle-a-S.  1900.     Beiblatter,  xxiv.  p.  1343. 
*     T.  G.  19 


290  BECQUEREL   RAYS.  [150 

intense  heating  could  be  explained  by  supposing  that  at  high 
temperatures  this  compound  is  changed  into  one  not  giving  the 
emanation,  the  change  being  a  permanent  one,  the  new  substance 
not  being  destroyed  by  the  subsequent  cooling. 

A  good  illustration  of  the  effect  of  changes  in  the  physical 
condition  of  the  substance  on  its  emanating  power  is  afforded  by 
the  nitrate ;  this  salt  when  in  the  solid  state  gives  out  but  little 
emanation,  when  however  the  salt  is  dissolved  in  water  and  air 
bubbled  through  the  solution  the  air  carries  off  more  than  200 
times  the  quantity  of  emanation  that  could  be  obtained  by  passing 
the  air  over  an  equal  quantity  of  the  solid ;  the  quantity  of 
emanation  obtained  by  bubbling  depends  only  upon  the  quantity 
of  the  salt  and  not  upon  the  degree  of  dilution. 

Source  of  the  Emanation. 

150.  Rutherford  and  Soddy  have  made  a  series  of  experi- 
ments to  see  whether  the  emission  of  the  emanation  is  a  property 
of  thorium  itself,  or  whether  it  is  due  to  some  impurity.  The  con- 
clusion they  came  to  was  that  it  was  not  emitted  directly  from  the 
thorium,  since  they  could  obtain  from  thorium  salts  substances 
whose  emanating  power  was  enormously  greater  than  that  of  the 
original  salt.  One  method  of  doing  this  was  to  dissolve  a  quantity 
— in  the  experiment  70  grams — of  thorium  nitrate  in  water  and 
precipitate  the  thorium  by  adding  ammonia.  The  nitrate  was  then 
evaporated  down  to  about  60  c.c.,  and  was  found  to  possess  when 
air  was  bubbled  through  it  as  much  emanating  power  as  146  grams 
of  thoria;  on  evaporating  to  complete  dryness  and  getting  rid  of 
the  ammonium  salts  the  residue  left  only  weighed  '0583  gram. 
Thus  this  residue  consisted  of  a  substance  which  when  in  solution 
gave  with  a  weight  of  '0583  gram  as  much  emanation  as 
146  grams  of  thoria,  or  weight  for  weight  its  emanating  power 
was  2500  times  that  of  thoria.  The  separation  of  this  substance 
was  accompanied  by  a  loss  in  the  emanating  power  of  the  sub- 
stance from  which  it  was  produced,  for  when  the  hydroxide  pre- 
cipitated in  this  experiment  was  converted  into  oxide,  the  ema- 
nating power  of  this  was  only  about  one-third  that  of  oxide 
prepared  from  nitrate  which  had  not  been  dissolved.  Similar 
results  were  obtained  by  testing  the  water  used  to  wash  the  oxide. 
Residues  were  obtained  by  evaporating  the  washings  to  dryness, 


151] 


BECQUEREL   RAYS. 


291 


and  some  of  these  residues  were  1800  times  more  radio-active  than 
the  original  thoria.  No  substance  other  than  thorium  could  be 
detected  in  these  residues ;  the  quantity  of  material  available  was 
however  too  small  to  admit  of  a  very  searching  examination. 

151.  In  a  subsequent  paper  Rutherford  and  Soddy*  have 
shown  that  the  very  active  residues  they  obtain  by  those  methods 
gradually  lose  their  radio-activity,  while  the  thorium  hydroxide 
which  had  been  deprived  of  its  power  by  the  abstraction  of  this 
residue  gradually  recovers  and  ultimately  regains  its  normal 
activity ;  thus  in  one  case  they  found  that  in  about  three  weeks 
the  recovery  of  the  hydroxide  whose  strength  had  been  reduced 
to  about  36  %  of  its  normal  value  was  practically  complete,  while 
the  residue  which  originally  was  so  abnormally  active  had  in  the 
same  time  lost  the  whole  of  its  activity.  This  led  to  a  series  of 
experiments  on  the  rate  of  recovery  of  the  hydroxide  and  the 
rate  of  loss  of  the  residue  called  by  them  Th  X,  the  residue  was 
prepared  by  the  ammonia  process  described  on  p.  290.  The 


No.  of  D 


J 


Fig.  76. 

results  of  these  experiments  are  shown  in  the  curves  given  in 
Fig.  76:   it  will  be  seen  that  the  time  taken  by  the  hydroxide 

*  Rutherford  and  Soddy,  Phil.  Mag.  vi.  4,  pp.  370,  569,  1902. 

19—2 


292  BECQUEREL   RAYS.  [151 

to  recover  half  of  its  lost  radio-activity  is  about  the  same  as  that 
taken  for  the  radio-activity  of  the  Th  X  (the  residue)  to  lose  half 
of  its  original  activity.  Rutherford  and  Soddy  by  these  experi- 
ments were  led  to  a  theory  of  radio-activity  which  explains  this 
and  many  other  phenomena.  This  view  is  as  follows;  the 
radio-active  constituent  in  the  thorium  compounds  is  not  an 
accidental  impurity,  but  is  a  substance  which  we  may  call  ThX, 
which  is  being  manufactured  at  a  constant  rate  from  the  thorium  ; 
after  its  manufacture  its  radio-activity  gradually  dies  away.  The 
normal  radio-activity  of  a  thorium  compound  is  due  to  a  state  of 
dynamical  equilibrium  in  which  the  increase  in  radio-activity  due 
to  the  production  of  fresh  ThX  just  balances  the  loss  due  to  the 
fading  away  of  the  activity  of  the  Th  X  previously  produced. 

To  put  this  in  a  mathematical  form  suppose  that  T  is  the 
amount  of  thorium  present  at  any  time,  let  the  amount  of  Th  X 
produced  by  this  in  unit  time  be  aT;  let  the  initial  radio-activity 
of  unit  mass  of  Th  X  be  r,  then  the  rate  at  which  the  radio- 
activity of  the  mixture  is  increasing  in  consequence  of  the  pro- 
duction of  fresh  Th  X  is  raT  ;  let  R  be  the  radio-activity  of  the 
mixture,  let  this  in  consequence  of  the  loss  of  energy  by  radiation 
be  decreasing  at  the  rate  \R  ;  then  we  have 


when  things  are  in  a  steady  state  dR/dt  vanishes  and  we  have 


. 

The  general  solution  of  (1)  is,  regarding  T  as  constant, 

R  =  ~  +  C€~M  .......................  (2) 

A, 

where  G  is  a  constant.  Let  us  suppose  that  we  remove  all  the 
Th  X  and  so  deprive  the  substance  of  its  radio-activity,  then 
initially  when  t  =  0,  R  =  0  and  (2)  becomes 


thus  the  compound  will  have  recovered  half  of  its  normal  activity 
when  e~M  =  J  or  when  t  =  -  log  2. 

A. 


152]  BECQUEREL    RAYS.  293 

Let  us  now  consider  the  radio-activity  of  the  Th  X  removed 
from  the  mixture,  as  there  is  no  thorium  in  the  mixture  T  =  0 
so  (2)  becomes 

R  =  Ce-A«, 

thus  the  intensity  of  the  radiation  will  fall  to  half  its  original 
value  when  e~M  =  £  or  when  t  =  -  log  2  ;  thus  the  time  taken  for 

A. 

the  Th  X  to  lose  half  its  radio-activity  is  equal  to  the  time  taken 
for  the  salt  from  which  the  Th  X  was  removed  to  recover  half  of 
its  lost  activity,  and  this  as  we  have  seen  is  approximately  the 
case. 

On  this  view  the  energy  required  t6  maintain  the  radiation  is 
obtained  from  the  chemical  change  which  is  taking  place  in  the 
thorium,  the  change  from  thorium  to  thorium  X  being  accompanied 
by  a  loss  of  energy. 

Rutherford  and  Soddy  consider  that  Th  X  is  a  distinct  sub- 
stance and  not  merely  some  chance  substance  that  may  have  been 
present  along  with  the  thorium  in  the  salt.  Their  reason  for 
thinking  that  the  latter  view  is  not  tenable  is  that  if  it  were 
true  then  any  method  of  precipitating  the  thorium  from  a  solution 
ought  to  leave  the  solution  radio-active  after  the  loss  of  the 
thorium ;  this  is  not  however  the  case,  it  is  only  certain  special 
methods  of  precipitation  which  deprive  the  precipitated  thorium 
of  its  activity  and  leave  the  solution  radio-active ;  this  implies 
that  the  substance  which  is  the  origin  of  the  radio-activity  is  one 
having  definite  chemical  properties. 

152.  Emanating  Power.  The  loss  of  radio-activity  of  the 
thorium  hydroxide  treated  in  the  way  described  above  is  accom- 
panied also  by  a  loss  of  emanating  power,  while  the  Th  X  possesses 
this  power  to  a  very  large  extent  when  first  formed :  it  is  found 
that  as  the  thorium  hydroxide  recovers  its  radio-activity  it  also 
recovers  pari  passu  its  emanating  power,  while  the  emanation 
from  the  Th  X  becomes  smaller  and  smaller  and  finally  dis- 
appears. This  is  what  would  happen  if  the  Th  X  split  up  after 
its  formation,  one  of  the  products  of  the  decomposition  being  the 
emanation. 

An  interesting  question  is  what  becomes  of  the  dead  Th  X 
and  the  dead  emanation ;  since  the  Th  X  is  only  active  for  about 


294 


BECQUEREL   RAYS. 


[153 


a  week,  the  amount  of  the  spent  Th  X  to  the  active  will  be  the 
ratio  of  the  age  of  the  thorium  compound  to  one  week.  As  the 
life  of  the  emanation  is  very  much  shorter  the  proportion  of  the 
spent  emanation  to  the  active  will  be  very  much  larger.  Is  it 
possible  that  the  gases  like  helium  and  argon  which  are  so  often 
found  in  minerals  containing  radio-active  substances  represent 
the  accumulations  of  spent  emanations  ?  The  chemical  inertness 
which  is  so  marked  a  feature  of  these  gases  is  also  as  we  have 
seen  a  characteristic  of  the  emanation. 

153.  Debierne*  by  extracting  the  thorium  from  pitchblende 
obtained  an  exceedingly  radio-active  product,  he  ascribed  this 
activity  to  the  presence  of  a  new  element,  which  he  named 
1  actinium ' ;  he  was  not  able  to  separate  the  actinium  from  the 
thorium. 


Induced  Radio-activity  produced  by  Thorium  Emanation. 

154.  Rutherford  f  discovered  that  the  emanation  from  thorium 
makes  any  substance  with  which  it  comes  in  contact  radio- 
active. This  can  be  shown  by  the  following  experiment  (Fig.  77). 


Fig.  77. 

Two  isolated  plates  B  and  C  are  placed  parallel  to  one  another 
in  a  closed  metallic  vessel  connected  with  the  earth.  In  a  shallow 
depression,  LM,  in  the  plate  (7,  a  layer  of  thorium  oxide  is  placed 
and  covered  with  several  layers  of  foolscap  paper.  The  plate  C 
is  connected  to  the  positive  pole  of  a  battery,  giving  a  potential 
difference  of  at  least  50  volts,  and  the  other  pole  of  this  battery 
is  connected  with  the  earth.  The  plate  B  is  connected  with  an 
electrometer.  If  this  is  left  for  several  hours,  and  then  the 

*  Debierne,  Comptes  Rendus,  cxxix.  p.  563,  1899 ;  cxxx.  p.  906,  1900. 
t  Rutherford,  Phil.  Mag.  v.  49,  p.  161,  1900. 


154] 


BECQUEREL   RAYS. 


295 


plate  C  with  the  thorium  removed,  and  replaced  by  a  clean 
metallic  plate,  it  will  be  found  that  the  gas  between  the  plates  now 
possesses  considerable  conductivity ;  this  will  gradually  diminish 
with  lapse  of  time  and  after  a  few  days  become  inappreciable. 
If,  instead  of  leaving  B  in  the  vessel  when  C  is  removed,  both 
B  and  C  are  replaced  by  fresh  plates,  there  will  be  no  conduc- 
tivity; the  ionisation  is  thus  due  to  some  change  produced  in 
the  plate  B  by  the  action  of  the  thorium.  The  plate  B  has  been 
made  radio-active.  That  this  effect  is  due  to  the  action  of  the 
emanation  and  not  of  the  straight  line  radiation  may  be  proved 
in  several  ways.  In  the  first  place,  the  effect  is  absent  if  we  use 
*a  thin  layer  of  thorium  oxide,  which  emits  plenty  of  straight  line 
radiation  but  very  little  emanation.  Again,  when  we  de-emanate 
thorium  oxide  by  intense  heating  (see  p.  289),  we  destroy  its 
power  of  producing  induced  radio-activity,  although  we  do  not 
affect  its  power  of  emitting  straight  line  radiation. 

The  close  connection  between  the  emanation  and  the  induced 
radio-activity  is  shown  by  the  following  experiment  made  by 
Rutherford. 

A  slow  current  of  air  from  a  gas-bag  passed  down  a  rect- 
angular wooden  pipe,  60  cm.  long ;  the  air  passed  through  sul- 
phuric acid  to  dry  it,  and  through  a  plug  of  cotton-wool  in  the 
pipe  at  W,  this  plug  removed  spray  and  equalised  the  flow  of 
air  over  the  cross  section  of  the  tube.  A  metal  plate  charged 
with  positive  electricity  covered  the  bottom  of  the  tube,  four 
insulated  metal  plates  A,  B,  C,  D,  placed  at  equal  intervals,  had 
a  negative  charge  induced  on  them  by  being  connected  with  the 
earth.  When  the  current  of  air  passed  through  the  vessel  with 
the  velocity  *2  cm./sec.  for  7  hours,  with  a  potential  difference  of 
300  volts  between  the  lower  and  upper  plates,  the  following 
results  were  obtained : 


Eelative  current  due 

Relative  excited 

to  emanation 

radio-activity 

Plate  A  ... 

1 

r 

„      B  ... 

•55 

•43 

„      C  ... 

•18 

•16 

„      I)- 

•072 

•061 

296  BECQUEREL   RAYS.  [155 

Thus  the  induced  radio-activity  is  approximately  proportional 
to  the  intensity  of  the  radiation  given  out  by  the  emanation. 

The  experiment  shows  that  the  emanation  is  in  some  way  the 
cause  of  the  induced  radio-activity ;  it  does  not  enable  us  to 
decide  whether  the  radio-activity  is  due  to  a  deposit  of  the 
substance  of  the  emanation  on  the  plate,  or  whether  it  is  due 
to  a  change  in  the  surface  layers  of  the  plate  produced  by  the 
radiation  coming  from  the  emanation.  We  shall  return  to  this 
point  when  we  have  discussed  more  fully  the  properties  of  the 
induced  radio-activity. 

If  in  the  inclosure  containing  the  thorium  and  the  emanation* 
there  is  a  conductor  strongly  charged  with  negative  electricity,  the 
induced  radio-activity  will  be  concentrated  on  this  conductor  and 
there  will  be  less  on  the  walls  of  the  inclosure  than  there  would 
be  if  the  conductor  were  uncharged ;  thus  the  excess  of  radio- 
activity on  the  wire  is  obtained  at  the  expense  of  that  on  the 
surrounding  objects. 

The  amount  and  quality  of  the  induced  radio-activity  seem  to 
be  independent  of  the  material  of  which  the  walls  of  the  inclosure 
are  made;  the  substitution  of  paper  or  cardboard  for  metal  makes 
no  appreciable  difference  in  the  result.  The  radio-activity  does 
not  depend  upon  the  nature  of  the  gas  in  the  inclosure,  nor  upon  the 
pressure  of  the  gas,  although  the  concentration  of  the  induced 
radio-activity  on  negatively  electrified  surfaces  is  less  complete  at 
low  pressures  than  it  is  at  high.  Thus,  for  example,  in  an  experi- 
ment made  by  Rutherford  the  induced  radio-activity  on  a  nega- 
tively electrified  wire  was  practically  unchanged  when  the  pres- 
sure was  reduced  from  760  mm.  to  16  mm.;  at  a  pressure  of  5  mm. 
however,  it  was  about  1/20  of  its  value  at  the  higher  pressure ; 
this  diminution  in  the  radio-activity  of  the  wire  is  accompanied 
by  an  increase  in  that  of  the  walls  of  the  inclosure. 

155.  Duration  of  the  induced  radio-activity.  This  induced 
radio-activity  dies  away  gradually  with  the  time ;  the  rate  of  de- 
crease is,  however,  very  slow,  as  Rutherford's  measurements  show 
that  it  takes  about  11  hours  for  the  intensity  of  the  radiation  to 
fall  to  1/2  of  its  original  value.  The  rate  at  which  the  radiation 
dies  away  does  not  depend  upon  the  nature  of  the  material  which 
is  made  radio-active.  The  duration  of  the  induced  radio-activity 


156]  BECQUEREL   RAYS.  297 

is  thus  very  much  greater  than  that  of  the  emanation  which  pro- 
duced it,  as  we  have  seen  that  this  fades  away  to  one-half  its 
original  value  in  one  minute.  We  must  remember,  however,  that 
this  relates  to  the  emanation  when  it  has  escaped  from  solids  and 
is  in  a  form  analogous  to  that  of  a  free  gas,  we  do  not  know  whether 
the  rate  of  decay  is  as  great  as  this  when  the  emanation  is  diffus- 
ing through  a  solid :  the  results  of  experiments  seem  rather  to 
indicate  that  it  is  not,  for  the  emanation  is  still  active  after  passing 
through  a  great  many  sheets  of  paper ;  if  its  rate  of  decay  when  in 
the  paper  is  as  rapid  as  it  is  when  in  the  air  it  must  be  able  to 
diffuse  through  these  in  a  very  few  minutes. 

A  surface  once  made  radio-active  can  be  exposed  to  very  rough 
usage  without  losing  this  property;  thus  Rutherford  raised  a  piece 
of  radio-active  platinum  to  a  white  heat  and  found  after  cooling 
that  it  had  lost  little  if  any  of  its  activity.  Washing  the  surface 
with  hot  or  cold  water,  caustic  soda,  or  nitric  acid  has  no  effect 
upon  the  activity ;  if,  however,  the  wire  is  dipped  in  sulphuric  or 
hydrochloric  acid  the  radio-activity  is  removed  in  a  few  minutes : 
the  radio-activity  is  however  only  removed  from  the  metal  to  the 
acid,  for  on  evaporating  down  to  dryness  the  residue  left  was  found 
to  be  strongly  radio-active.  It  would  thus  appear  that  the  radio- 
active substance  is  dissolved  in  the  acid  and  retains  its  radio- 
activity. 

No  change  in  weight  due  to  the  induced  radio-activity  can  be 
detected,  nor  does  microscopic  examination  of  the  metal  reveal 
the  presence  of  any  dust  or  any  change  in  the  surface.  The  radio- 
activity can  be  removed  by  long  scouring  with  sand  or  emery 
paper,  the  pieces  removed  are  radio-active. 

156.  Time  taken  to  produce  the  Radio-activity.  The  radio- 
activity takes  considerable  time  to  produce.  On  first  exposure  to 
the  emanation  it  increases  nearly  proportionally  with  the  time, 
afterwards  the  rate  of  increase  falls  off,  and  it  ultimately  attains  a 
constant  value.  The  following  diagram  (from  Rutherford's  paper) 
shows  how  the  intensity  of  the  induced  radiation  increases  with 
the  time  of  exposure  to  the  thorium. 

The  time  taken  to  attain  a  steady  state  is  fixed  by  the  rate  at 
which  the  induced  radiation  fades  away.  For  let  I  be  the  inten- 
sity of  the  induced  radio-activity  at  any  time  t,  q  the  rate  at  which 


298 


BECQUEREL   RAYS. 


[156 


this  is  increasing  in  consequence  of  the  presence  of  the  thorium, 
I  IT  the  rate  at  which  it  would  decay  if  no  thorium  were  present, 
then  we  have 

dl  I 


or 


I  =  qT(l-e~lr 


thus  the  radio-activity  will  not  reach  a  steady  state   until  t  is 
considerably  greater  than  T.     Now   T  has  been  determined  by 


100 


90 


30 


20 


10 


77/r»e    ,n 


0         10       20       30       40       50       60       70       80       90      100 
Fig.  78. 

Rutherford  by  measuring  the  rate  at  which  the  activity  of  the 
surface  disappears  when  it  is  not  exposed  to  the  action  of  thorium; 
putting  q  =  0  we  get 


where  /0  is  the  value  of  /  when  t  =  0 ;  Rutherford  found  that  /  fell 
to  £/0  in  about  11  hours,  so  that  T=  16  hours ;  thus  it  will  take  a 
time  greater  than  11  hours  but  comparable  with  it  for  the  induced 
radio-activity  to  reach  a  steady  state.  We  see  from  equation  (1) 
that  the  induced  radio-activity  should  reach  half  its  final  value  in 
about  11  hours;  an  inspection  of  Fig.  78  will  show  that  this  is 
the  case. 


157]  BECQUEREL   RAYS.  299 

Penetrating  power  of  the  induced  Radio-activity. 

157.  Rutherford  measured  the  penetrating  power  of  the  in- 
duced radiation  and  found  that  it  was  considerably  greater  than 
that  from  thin  layers  of  the  thorium  itself.  Thus  the  latter  is 
reduced  to  half  its  intensity  after  passing  through  about  1  cm.  of 
air  at  atmospheric  pressure,  while  the  induced  radio-activity  can 
pass  through  1*65  cm.  before  its  intensity  is  reduced  by  the  same 
amount.  The  penetrating  power  of  the  induced  radio-activity  is 
independent  of  the  nature  of  the  substance  made  radio-active; 
this  is  a  strong  indication  that  the  induced  radio-activity  is  due 
to  a  deposit  of  the  emanation  and  not  to  an  alteration  of  the  sur- 
face of  the  substance  by  radiation  from  the  emanation.  Further 
evidence  on  this  point  could  probably  be  obtained  by  observing 
at  different  air  pressures  the  distances  from  the  thorium  at  which 
a  substance  can  be  made  radio-active.  For  if  it  is  due  to  a 
deposit  of  the  emanation  the  experiment  described  on  p.  295  shows 
that  the  emanation  must  be  deposited  while  it  is  radio-active,  i.e., 
not  much  longer  than  a  minute  after  it  has  left  the  thorium. 
If  the  substance  to  be  made  radio-active  is  placed  so  far  away 
from  the  thorium  that  the  emanation  takes  much  more  than 
a  minute  to  diffuse  to  it,  the  emanation  will  be  spent  before  it 
reaches  the  surface  and  this  will  not  become  radio-active.  Now 
the  distance  through  which  the  emanation  can  diffuse  in  a  time  T 
is  proportional  to  V DT  where  D  is  the  coefficient  of  diffusion  of 
the  emanation;  as  D  varies  inversely  as  the  pressure  of  the  gas  the 
distance  at  which  a  surface  could  become  radio-active  would  be 
inversely  proportional  to  the  square  root  of  the  pressure.  If, 
however,  the  induced  radio-activity  were  due  to  the  radiation 
given  out  by  the  emanation,  then  since  the  transparency  of  a 
gas  to  the  radiation  is  inversely  proportional  to  the  pressure  the 
distance  at  which  a  surface  could  be  made  radio-active  would 
be  inversely  proportional  to  the  pressure  and  not,  as  in  the  pre- 
ceding case,  to  the  square  root  of  the  pressure. 

The  effect  produced  by  negative  electrification  in  increasing 
the  induced  radio-activity  on  a  surface  thus  electrified  is,  I  think, 
probably  connected  with  the  property  possessed  by  several  radio- 
active substances,  for  example  uranium  and  radium,  of  emitting 
negatively  electrified  corpuscles.  Let  us  trace  the  consequences 


300 


BECQUEREL   RAYS. 


[158 


of  supposing  that  the  radio-active  emanation  from  thorium  pos- 
sesses this  property.  As  the  radio-activity  of  the  particles  we 
have  seen  only  lasts  for  a  short  time,  it  is  probable  that  most  of 
the  particles  will  be  spent  before  they  have  time  to  emit  these 
negative  corpuscles.  But  the  particles  which  succeed  in  doing 
this  and  which  thereby  acquire  a  charge  of  positive  electricity 
will  now  be  attracted  by  the  negatively  electrified  surface  and  will 
move  rapidly  up  to  it.  The  velocity  with  which  the  particle 
moves  in  the  electric  field  is  very  great  compared  with  the  velocity 
with  which  it  would  have  moved  towards  the  surface  if  only  diffu- 
sion had  come  into  play.  Thus  the  emanation  will  in  consequence 
of  the  charge  on  the  surface  arrive  at  the  surface  very  much 
sooner  than  it  would  have  done  if  there  had  been  no  charge ;  it 
thus  arrives  very  much  fresher  and  is  much  more  efficient  as  a 
producer  of  induced  radio-activity. 

158.  The  velocity  acquired  by  the  positively  charged  particles 
of  the  emanation  when  in  the  electric  field  has  been  measured  by 
Rutherford*,  using  the  following  method,  which  is  based  on  the 
assumption — justified  by  the  extent  to  which  the  induced  radio- 
activity can  be  concentrated  on  a  negatively  electrified  surface- 
that  the  radio-activity  of  the  surface  is  almost  wholly  due  to  the 
number  of  positively  electrified  particles  which  reach  it. 

The  emanation  spreads  between  two  parallel  plates  A  and  B, 
Fig.  79,  an  electric  field  is  produced  between  the  plates,  this  field 


Fig.  79. 

consists  of  two  parts,  (1)  a  constant  potential  difference  equal  to 
E0  making  the  top  plate  +,  the  lower  plate  — ,  (2)  a  field  in  which 


Rutherford,  Physikalische  Zeitschrift,  iii.  p.  210, 1902;  Phil.  Mag.  vi.  5,  p.  95, 1903. 


158]  BECQUEREL   RAYS.  301 

the  direction  of  the  force  is  reversed  at  equal  intervals  of  time  T ; 
thus  it  is  equal  to  E^  for  a  time  T,  then  changes  to  —  El  which  lasts 
for  a  time  T,  when  it  changes  again  to  -f  El  and  so  on.  This 
variable  potential  difference  is  placed  in  series  with  the  constant 
potential  difference,  so  that  in  the  first  half  of  the  alternation  the 
electric  force  acting  downwards  is  (E^-^-E^jd  where  d  is  the  dis- 
tance between  the  plates,  while  in  the  second  half  of  the  alterna- 
tion it  is  equal  to  (El  —  E0)/d  and  acts  upwards:  El  is  supposed 
to  be  greater  than  E0.  There  is  thus  on  the  average  a  tendency 
to  make  the  positive  ions  go  to  the  lower  plate,  but  during  the 
second  half  of  the  alternation  some  of  the  particles  will  be  attracted 
to  the  upper  plate  and  will  make  it  radio-active :  the  number  of 
such  particles  will  depend  upon  the  velocity  of  the  particles  and 
may  be  calculated  as  follows. 

Let  K  be  the  velocity  of  the  particles  under  unit  electric  force 
and  let  us  suppose  that  the  positive  particles  are  being  produced 
uniformly  between  the  plates,  the  number  produced  in  one  second 
in  a  layer  of  unit  thickness  between  the  plates  being  q.  The 
particles  which  reach  the  upper  plate  when  negatively  electrified 
will  be  of  two  classes:  (1)  those  produced  whilst  the  plate  is  nega- 
tively electrified,  and  (2)  those  which  were  present  between  the 
plates  at  the  beginning  of  the  alternation.  Let  us  take  first  the 
number  in  the  first  class;  consider  the  number  sent  to  the  top 
plate  by  a  layer  of  thickness  dx  at  a  distance  x  away  from  it,  any 
particle  from  this  layer,  since  it  moves  with  the  velocity  J£Xl}  will 
take  the  time  xj  KX^  to  reach  the  plate.  Xl  is  the  electric  force 
between  the  plates  and  is  equal  to  (El  —  £0)/d.  Since  the  particle 
must  reach  the  plate  before  the  end  of  the  alternation  the  latest 
time  it  can  start  is  xjKX-^  before  the  end,  and  thus  the  particles 
reaching  the  layer  are  only  formed  for  a  time  T—xjKX^  thus 
the  number  of  particles  reaching  the  plate  from  this  layer  is 
q(T -xjKX^dx  and  the  total  number  of  particles  in  class  (1)  is 
equal  to 


CKX.T 

JO 


The  number  in  class  (2)  will  be  the  number  of  positive  particles 
at  the  beginning  of  the  alternation  in  a  layer  next  the  upper  plate 
whose  thickness  is  KXl  T.  The  force  in  the  preceding  alternation 


302  BECQUEREL   RAYS.  [158 

tending  to  drive  the  particles  from  the  upper  plate  is  X2  where 
X2  =  (E0  4-  -fi'i)  /  d  :  hence  the  velocity  of  the  particles  is  KXZ:  the 
number  of  particles  produced  in  a  layer  of  thickness  dx,  at  a  dis- 
tance x  from  the  upper  plate,  which  have  not  moved  by  the  end 
of  the  alternation  to  a  distance  from  the  upper  plate  greater  than 


XX  l  T  is  q  -  -  £=.  —  —  dx  ;  hence  the  number  of  particles  in  the 
jfx-A2 

second  class  is  equal  to 


=  1    K.X*T* 

Thus  the  total  number  of  positive  particles  reaching  the  upper 
plate  in  the  time  of  a  double  alternation  of  length  ZT 


In  this  time  the  total  number  of  positive  particles  produced  is 
2qdT,  and  if  care  is  taken  to  make  the  electric  field  sufficiently 
strong  all  these  particles  will  reach  one  or  other  of  the  plates. 
Hence  p  the  ratio  of  the  number  of  particles  reaching  the  upper 
plate  to  the  sum  of  the  numbers  reaching  the  upper  and  lower 
plates  is  given  by  the  equation 


or  substituting  for  X1  and  X2  their  values  we  get 


On  the  hypothesis  already  mentioned,  that  the  induced 
radio-activity  is  almost  entirely  caused  by  the  positively  charged 
particles  which  come  up  to  the  plate,  p  is  the  ratio  of  the 
radio-activity  of  the  upper  plate  to  the  sum  of  the  activities  of 
the  upper  and  lower  plates,  and  by  measuring  these  activities  p 
can  be  determined  ;  when  p  is  known  equation  (1)  gives  us  the 
means  of  determining  K  and  hence  the  velocity  of  the  positively 
charged  particles  in  an  electric  field.  By  this  method  Kutherford 
got  the  following  results. 


158] 


BECQUEREL   RAYS. 

Plates  1*3  cm.  apart. 


303 


E!+E 

volts 

E!-JB 

volts 

Alternations 
per  sec. 

p 

Velocity  for  one 
volt  per  cm. 

152 

101 

57 

•27 

1-25 

225                     150                        57 

•38 

1-17 

Plates  2  cm.  apart. 

272 

207 

44 

•37 

1-47 

300 

200 

53 

•286 

1-45 

These  results  relate  to  air  at  atmospheric  pressure.  Zeleny 
(p.  47)  found  that  the  velocity  of  the  positive  ion  produced  by 
Rontgen  rays  in  air  at  this  pressure  was  T36  cm. /sec.  for  the 
potential  gradient  of  a  volt  per  cm. :  the  velocity  of  the  positive 
particles  in  the  thorium  emanation  is  thus  within  the  limits  of 
experimental  errors  equal  to  the  velocity  of  the  ordinary  positive 
ions. 

Rutherford  has  shown  that  at  low  pressures,  say  less  than  1  mm., 
of  mercury  there  is  less  tendency  for  the  radio-activity  to  be  con- 
centrated on  the  negative  electrode  than  there  is  when  the  pressure 
is  higher.  We  see  that  if  the  mean  free  path  of  the  particle  were 
comparable  with  the  size  of  the  vessel  there  ought  not  on  the 
preceding  view  to  be  much  concentration  unless  the  particles 
were  at  rest,  or  at  any  rate  were  moving  with  a  velocity  small 
compared  with  that  which  would  be  developed  by  the  movement 
of  the  charged  particles  through  a  fall  of  potential  equal  to  that 
between  the  negatively  electrified  body  and  the  walls  of  the  vessel : 
for  it  is  only  in  the  latter  case  that  the  particle  would  strike 
the  attracting  body,  in  all  others  it  would  describe  an  orbit  round 
it  and  would  strike  the  walls  of  the  vessel  and  not  the  electrode 
itself. 

Radio-activity  of  Radium,  Polonium,  Actinium. 

The  Becquerel  rays  have  led  to  the  discovery  of  some  new  sub- 
stances possessing  the  power  of  radio-activity  to  a  far  greater 
extent  than  uranium — the  original  source  of  these  rays,  After 
Becquerel's  discovery  Monsieur  and  Madame  Curie*  made  a  very 

*  Curie,  Rapports,  Congres  International  de  Physique,  t.  iii.  p.  79,  Paris,  1900. 


304 


BECQUEREL   RAYS. 


[158 


systematic  and  extensive  examination  of  a  great  number  of 
chemical  elements  and  compounds,  and  also  of  minerals,  to  see 
if  other  elements  possessed  powers  similar  to  uranium ;  the  ex- 
amination of  the  elements  and  compounds  (which  included  the 
rare  elements,  gallium,  germanium,  neodydymium,  praseodydy- 
mium,  mobium,  scandium,  gadolinium,  erbium,  samarium,  rubi- 
dium, yttrium,  ytterbium,  holmium)  did  not  lead  to  the  discovery 
of  any  substances  other  than  uranium  possessing  this  property. 
The  investigation  of  the  minerals  was  more  fruitful,  for  they  found 
that  several  minerals  containing  uranium  were  more  active  than 
the  same  bulk  of  uranium.  This  is  shown  by  the  following  table 
in  which  i  is  the  saturation  current  in  amperes  between  two  circular 
plates  8  cm.  in  diameter  and  3  cm.  apart  when  one  of  the  plates 
is  covered  with  the  substance  under  consideration : 


i  x  1011  amperes 

i  xlO11  amperes 

Metallic  Uranium 

2-3 

Thorite 

1-4 

Pitch-blende  from 

Orangeite    

2-0 

Johanngeorgeustadt 

8-3 

Monazite  

0-5 

Joachimstal 

7-0 

Xenotime 

0-03 

Pribran  

6-5 

^Eschynite  . 

0'7 

Cornwall     

1-6 

Fergusonite    

0'4 

Cleocite 

1-4 

Samarskite 

1-1 

Chalcolite 

5-2 

Niobite 

0-3 

Autunite    

2-7 

Carnotite 

6'2 

All  these  minerals  contain  uranium  and  thorium,  but  it  will 
be  seen  that  several  of  them  are  more  radio-active  than  the  pure 
metals :  this  suggests  that  they  may  contain  some  exceedingly 
active  substantives  other  than  uranium,  this  supposition  was 
strengthened  when  Monsieur  and  Madame  Curie  prepared  Chal- 
colite artificially  from  pure  substances  and  found  that  it  was  only 
about  one-fifth  as  radio-active  as  the  natural  mineral.  They  then 
set  to  work  to  search  pitch-blende  systematically;  they  tested  the 
radio-activity  of  a  certain  piece,  then  separated  this  chemically 
and  tested  that  of  the  constituents,  and  thus  gradually  separated 
the  active  from  the  inert  parts  of  the  pitch-blende.  This  treat- 
ment has  led  to  the  discovery  of  three  different  strongly  radio- 
active constituents  of  pitch-blende;  radium  discovered  by  Monsieur 
and  Madame  Curie  and  Monsieur  Bemont*,  polonium  discovered 
*  Curie  and  Bemont,  Comptes  Rendus,  cxxvii.  p.  1515,  1898. 


158] 


BECQUEREL    RAYS. 


305 


by  Monsieur  arid  Madame  Curie*,  and  actinium  by  Monsieur 
Debiernef.  Radium  accompanies  the  barium  prepared  from 
pitch-blende,  and  in  its  chemical  actions  is  similar  to  that  metal ; 
it  can,  however,  be  separated  from  barium  by  fractionation,  as  its 
chloride  is  less  soluble  in  water,  in  alcohol  and  in  hydrochloric 
acid.  The  amount  of  radium  in  pitch-blende  is  exceedingly  small, 
many  thousand  kilograms  of  this  mineral  only  yielding  a  few 
decigrams  of  a  radio-active  substance,  of  which  only  a  small  fraction 
is  radium.  The  spectrum  of  radium  was  examined  by  Dema^ayJ: 
the  following  are  the  principal  lines  between  wave-lengths  5000 
and  3500. 


Wave-length 

Intensity 

Wave-length 

Intensity 

4826-3 

10 

4600-3  ? 

3 

4726-9 

5 

4533-5 

9 

4699-8 

3 

4436-1 

8 

4692-1 

7 

4340-6 

12 

4683-0 

14 

3814-7 

16 

4641-9 

4 

3649-6 

12 

There  are  also  two  nebulous  bands  in  the  spectrum,  one  ex- 
tending from  4631*0  to  4621*9   with  the  maximum    at   4627*5; 


i 


Fig.  80. 


the  second  begins  suddenly  at  4463'7,  has  a  maximum  from  4455"2 
to  4453'4,  fading  away  at  4390.  The  appearance  of  the  spectrum 
is  shown  in  Fig.  80. 

The  sensitiveness  of  the  test  by  radio-activity  is  shown  by  the 
fact  that  it  required  several  thousand  times  more  radium  to  give 

*  Curie,  op.  cit.  p.  175. 

t  Debierne,  Comptes  Rendus,  cxxix.  p.  593,  1899 ;  cxxx.  p.  906,  1900. 

J  Demar(;ay,  Ib.  cxxvii.  p.  1218,  1898 ;  cxxix.  p.  116,  1899 ;  cxxxi.  p.  258,  1900. 

T.  G.  20 


306  BECQUEREL   RAYS.  [158 

an  appreciable  spectrum  than  to  give  an  amount  of  radio-activity 
quite  appreciable  by  electrical  methods. 

The  atomic  weight  of  radium  has  been  determined  by  Mon- 
sieur and  Madame  Curie*  to  be  225.  Runge  and  Prechtf  from 
consideration  based  on  its  spectrum  estimate  the  atomic  weight 
as  257-8. 

The  radiation  from  radium  is  extraordinarily  intense.  Mon- 
sieur and  Madame  Curie  have  prepared  specimens  of  radium 
which  when  enclosed  in  a  lead  tube  '5  cm.  thick  will  discharge  an 
electroscope  more  readily  than  uranium,  even  although  the  latter 
is  brought  without  any  covering  close  up  to  the  electroscope. 

The  radiation  comprises  rays  of  three  classes':  (1)  easily 
absorbed  rays  not  deflected  by  a  magnet  nor  by  an  electric  field f, 

(2)  much  more  penetrating  rays  which  are  deflected  by  magnetic 
or  electric  fields  and  which  carry  a  charge  of  negative  electricity, 

(3)  rays  still  more  penetrating  which  are  not  deflected. 

All  the  radium  salts  are  luminous  and  retain  this  property  for 
long  periods:  Giesel§  found  that  the  luminosity  diminished  in 
damp  air  but  recovered  its  brightness  on  drying. 

The  activity  of  the  radium  salts  like  some  of  those  of  thorium 
(see  p.  289)  increases  for  some  time  after  precipitation.  The  fol- 
lowing numbers  are  given  by  Curie  ;  initial  activity  95,  after  1  day 
120,  after  2  days  165,  after  3  days  210,  after  9  days  310,  after 
24  days  381,  after  300  days  410.  If  the  chloride  after  attaining 
its  maximum  activity  is  dissolved  and  reprecipitated  the  activity 
of  the  new  product  diminishes  as  the  time  it  is  kept  in  solution/ 
increases;  it  reaches,  however,  a  limit  after  the  salt  has  been  four 
or  five  days  in  solution.  It  would  be  interesting  to  know  if  the 
increase  in  activity  observed  for  some  time  after  the  preparation 
of  the  radium  compounds  occurs  in  all  the  three  classes  of  rays 
given  out  by  these  substances  or  is  confined  to  one  class. 

*  Curie,  Comptes  Rendus,  July  21,  1902. 

t  Eunge  and  Precht,  Physik.  Zeit'.  iv.  p.  285,  1903. 

£  Rutherford  has  quite  recently  shown  that  the  rays  of  class  1  are  slightly 
deflected  by  magnetic  or  electric  fields  and  that  they  carry  a  positive  charge ;  he 
found  that  the  velocity  of  these  rays  was  of  the  order  2  x  109  cm. /sec.  and  ejm  of 
the  order  6  x  103.  Phil.  Mag.  vi.  5,  p.  177,  1903.  Strutt  (Phil.  Trans.,  A,  1901, 
vol.  cxcvi.  p.  525)  had  previously  suggested  that  the  undeflected  rays  consisted  of 
positive  ions. 

§  Giesel,  Wied.  Ann.  Ixix.  p.  91,  1899. 


159] 


BECQUEREL  RAYS. 


307 


159.  The  magnetic  deflection  of  rays  given  out  by  some  radio- 
active substances  was  observed  almost  simultaneously  by  Giesel*, 
Meyer  and  v.  Schweidlerf,  and  Becquerel*.  Giesel  used  impure 
polonium  (polonium  free  from  radium  does  not  give  deviable 
rays),  Meyer  and  v.  Schweidler  impure  polonium  and  radium,  and 
Becquerel  radium.  Becquerel's  experiments  on  radium,  proving 
both  the  magnetic  and  electric  deflections  of  the  rays  and  showing 
that  these  deviable  rays  consist  of  corpuscles  projected  with  a 
velocity  about  two-thirds  of  that  of  light,  have  already  been  de- 
scribed. M.  and  Mme  Curie§  showed  that  radium  gave  out  non- 
deviable  as  well  as  deviable  rays  and  that  the  former  were  much 
more  easily  absorbed  than  the  latter.  The  arrangement  they  used 
is  represented  in  Fig.  81.  A  is  the  radio-active  substance  placed 


BATTED. 


B' 


Fig.  81. 

between  blocks  of  lead,  B,  B',  the  radiation  from  A  passes  be- 
tween these  blocks  into  the  space  between  the  parallel  plates 
P,  P',  making  the  air  between  these  a  conductor  and  allowing  a 
current  to  pass  between  the  plates,  the  magnitude  of  the  current, 
serving  as  a  measure  of  the  intensity  of  the  radiation  reaching  the 
space  between  the  plates.  P  is  charged  up  to  500  volts  and  P' 
connected  with  an  electrometer.  The  arrangement  B,  B',  B"  can 

*  Giesel,  Wied.  Ann.  Ixix.  p.  831,  1899. 

t  Meyer  and  v.  Schweidler,  Wien.  Ber.  p.  323,  1899.    Physik.  Zeitsc^r.  i.  p.  113, 
1899. 

£  Becquerel,  Comptes  Eendus,  cxxix.  p.  997,  1899. 
§  Curie,  16.  cxxx.  p.  73,  1900. 

20—2 


308  BECQUEREL   RAYS.  [160 

be  placed  between  the  poles  of  an  electro- magnet  which  produces 
a  strong  magnetic  field  at  right  angles  to  the  plane  of  the  paper ; 
if  the  rays  are  deflected  even  to  a  slight  extent  they  will  strike 
against  the  block  B,  B'  and  be  suppressed. 

The  effects  produced  by  the  magnet  depend  essentially  upon 
the  distance  AD  between  the  radio-active  substance  and  the 
place  where  it  is  tested ;  if  this  distance  is  greater  than  7  cm.  all 
the  rays  are  suppressed  by  a  magnetic  field  of  2500  units ;  at  a 
distance  of  6' 5  centimetres  only  a  portion  of  the  rays  are  sup- 
pressed and  this  portion  gets  smaller  and  smaller  as  the  plates 
P  and  P'  approach  the  radio-active  substance  A  ;  that  the  escape 
of  the  rays  from  the  magnetic  field  is  not  due  to  a  deficiency  in 
the  strength  of  the  field  is  shown  by  the  fact  that  when  the  mag- 
netic field  is  on  no  further  diminution  in  the  current  is  produced 
when  the  strength  of  the  field  is  increased  from  2500  to  7000 
units.  The  following  numbers  show  the  effects  observed  at  dif- 
ferent distances,  the  current  when  the  magnetic  field  is  off  being 
taken  as  100,  so  that  the  numbers  representing  the  current  with 
the  field  on  may  be  taken  as  the  percentage  of  non-deviable  rays 
which  are  able  to  penetrate  the  various  distances  through  air  at 
atmospheric  pressure. 

Distance  AD  in  centimetres  7'1,  6'9,  6'5,  6'0,  51,  3'4 
Current  with  magnet  on  0,     0,  11,  33,  56,   74 

If  the  radio-active  substance  is  covered  with  a  piece  of  thin 
aluminium  foil  or  a  piece  of  black  paper  all  the  non-deviable  rays  are 
absorbed  by  it  and  the  current  is  completely  stopped  by  the  mag- 
netic field.  It  will  be  seen  from  the  preceding  figures  that  only  a 
small  fraction  of  the  total  ionisation  produced  by  the  radium  is 
due  to  the  rays  which  are  deflected  by  a  magnet;  by  far  the  larger 
part  of  it  is  produced  by  the  non-deviable  easily  absorbed  rays. 

160.  That  these  deviable  rays  carry  a  charge  of  electricity  is 
proved  by  the  fact  discovered  by  Becquerel  (see  p.  Ill)  that  they 
are  deflected  when  placed  in  an  electric  field,  a  fact  also  observed 
by  Dorn*.  M.  and  Mme  Curie f  had  previously  shown  by  direct 
experiment  the  existence  of  the  negative  charge  on  these  rays.  If 
we  place  a  body  near  a  sample  of  radium  surrounded  by  air  at 

*  Dorn,  Comptes  Rendus,  cxxx.  p.  1126,  1900. 
t  Curie,  16.  p.  647. 


160]  BECQUEREL  KAYS.  309 

atmospheric  pressure  we  cannot  expect  to  observe  any  appreciable 
negative  charge  on  the  body,  for  the  radium  makes  the  air  a  con- 
ductor so  that  the  electricity  escapes  from  the  body  through  the 
air  as  fast  as  it  arrives.  To  observe  the  effect  we  must  work  in  a 
high  vacuum  where  there  is  not  enough  gas  to  produce  appreciable 
conductivity  or  else  replace  the  air  by  a  solid  dielectric;  the  Curies 
employed  the  latter  method ;  the  arrangement  they  used  is  shown 
in  Fig.  82.  A  metal  disc  MM  is  connected  by  a  wire  with  an 


Fig.  82. 

electrometer,  the  disc  and  wire  being  completely  surrounded  by  a 
solid  insulator, — ebonite  or  paraffin, — the  whole  is  placed  in  a 
metallic  case  connected  with  the  earth,  the  layer  of  insulating 
material  and  the  metal  of  the  case  are  very  thin  next  the  lower 
face  of  the  disc  MM.  This  lower  face  is  exposed  to  the  radiation 
from  the  radium  R  placed  in  a  cavity  in  a  block  of  lead  A  A.  It 
is  found  that  under  these  circumstances  the  disc  receives  a  con- 
stant stream  of  negative  electricity.  This  current  is  only  small; 
from  a  layer  of  radium  with  a  surface  of  2'5  sq.  cm.  and  *2  cm. 
thick,  and  with  the  rays  passing  on  their  way  to  the  disc  through 
aluminium  foil  "01  mm.  thick  and  a  layer  of  ebonite  *3  mm.,  the 
current  was  10~n  amperes. 

The  Curies  also  detected  the  positive  charge  left  behind  on 
the  radium ;  to  do  this  they  connected  the  lead  containing  the 
radium  with  the  electrometer  and  surrounded  it  by  an  insulating 
substance  as  is  shown  in  Fig.  82 ;  under  these  circumstances  they 
found  that  the  electrometer  received  a  positive  charge. 

Since  e/m  =  10~7  a  current  of  10~n  amperes  from  the  radium 
corresponds  to  a  loss  in  weight  of  about  one  three-hundredth  part 
of  a  milligram  in  a  million  years. 

No  charge  could  be  detected  on  the  non-deviable  rays,  but 
with  those  rays  on  account  of  the  great  absorption  the  experiment 
is  exceedingly  difficult. 


310 


BECQUEREL  RAYS. 


[161 


161.  The  properties  of  the  deviable  rays,  i.e.  their  deflection 
by  magnetic  and  electric  fields,  and  the  possession  of  a  negative 
charge  show  that  like  the  cathode  rays  they  consist  of  negatively 
electrified  corpuscles  moving  with  great  velocities ;  the  velocity  of 
some  of  the  particles  projected  from  radium,  viz.  2  x  1010cm./sec.,  is 
greater  than  that  we  have  yet  been  able  to  give  to  any  corpuscles 
by  purely  electrical  means.  Additional  confirmation  of  the  simi- 
larity between  the  deviable  radium  rays  and  cathode  rays  is  given 
by  the  study  of  the  absorption  of  these  rays  by  various  bodies. 
Lenard*  showed  that  if  a  bundle  of  cathode  rays  is  travelling 
parallel  to  the  axis  of  as,  and  if  70  is  the  intensity  of  the  rays 
when  #  =  0  and  /  the  intensity  after  travelling  a  distance  x, 
then  /  =  /0e^Aa;,  where  X  is  a  constant,  called  the  coefficient  of 
absorption  of  the  cathode  rays.  By  testing  a  great  number  of 
substances  with  densities  varying  from  that  of  solid  platinum  to 
that  of  hydrogen  gas  at  3  mm.  pressure,  Lenard  found  that  what- 
ever the  state  of  the  substance  might  be,  solid  or  gaseous,  X  was 
very  approximately  proportional  to  the  density  of  the  substance ; 
how  nearly  this  law  holds  will  be  seen  from  the  following  table  in 
which  X  is  the  coefficient  of  absorption  and  d  the  density ;  the 


Substance 

X  cm."1 

d  .  gr./cm.3 

X/d 

Hydrogen  at  3  mm.  pressure... 
Air  at  *78  mm.  pressure  

•00149 
•00416 

3-6xlO-7 
l'2x  10~6 

4040 
3330 

Hydrogen  at  760  mm.  pressure 

Air                                                                 ' 
-™-11                   »                »                55 

SOg                          55                        55                        55 

•476 
3-42 
8-51 
3310 

8-5  xlO-6 
1-2  x  10~3 
2-7xlO-3 
1*1 

5610 
2780 
3110 
3010 

2690 

1-30 

2070 

Glass  

7810 

2-47 

3160 

Aluminium           

7150 

2'70 

2650 

7250 

2  '80 

2590 

Dutch  Metal  

23800 

8-90 

2670 

Silver  

32200 

10-5 

3070 

Gold  

55600 

19-3 

2880 

rays  were  produced  by  a  tube  for  which  the  potential  difference 
between  the  electrodes  was  about  that  which  would  produce  a 
spark  in  air  about  2'8cm.  long:  from  some  later  determinations 


*  Lenard,  Wied.  Ann.  Ivi.  p.  255,  1895. 


161] 


BECQUEREL   RAYS. 


311 


made  by  Lenard*,  I  should  conclude  that  this  corresponded  to  a 
velocity  of  the  cathode  rays  of  about  6  x  109cm./sec. 

Thus  though  the  density  of  the  lightest  substance  is  only 
about  one  sixty-millionth  of  that  of  the  heaviest,  the  values  of 
\/d  only  range  from  2070  to  5610 :  and  if  we  leave  out  hydrogen, 
which  as  we  shall  see  exhibits  peculiarities  in  its  absorption  of 
all  rays,  the  range  is  only  from  2070  to  3330 ;  considering  the 
difficulties  of  the  experiment  this  is  strong  evidence  in  favour  of 
\jd  being  very  nearly  constant. 

R.  J.  Strutt  {•  has  measured  the  coefficient  of  absorption  of  the 
deviable  radium  rays  for  a  considerable  number  of  substances ;  his 
results  are  given  in  the  following  table. 


Substance 

X 

d 

\jd 

Platinum 

157-6 

21-5 

7-34 

Lead 

62-5 

11-4 

5-48 

Silver  

657 

10-6 

6'20 

Copper    

49-2 

8-95 

5-50 

Iron 

52-2 

776 

6'74 

Tin 

51-2 

7-3 

7-01 

Zinc  

40-3 

7-2 

5'58 

Mica    

10-8 

2-74 

3-94 

Glass 

12-5 

2*73 

4'58 

Aluminium  

11-6 

2-7 

4-30 

Celluloid  

5-45 

1-36 

4-01 

Ebonite  

4-77 

1-14 

4-18 

Card 

3-84 

ro 

3-84 

Sulphur  dioxide... 

•0413 

•00758 

5-45 

Thus  though  there  is  a  very  wide  range  in  the  values  of  X  and 
d,  the  values  of  \/d  differ  comparatively  little  from  each  other. 
The  coefficients  of  absorption  for  the  cathode  rays  are  roughly  about 
500  times  those  for  the  radium  rays ;  this  difference  is  probably 
due  to  the  much  greater  velocity  of  the  radium  rays,  which  wa,s 
found  by  Becquerel  to  be  as  great  as  2  x  1010  cm. /sec.,  while  the 
velocity  of  the  cathode  rays  used  by  Lenard  was  probably  only 
about  one-quarter  of  this. 

StruttJ  has  made  a  series  of  measurements  of  the  amount  of 
ionisation  produced  by  the  two  types  of  radium  rays  and  the 

*  Lenard,  Wied.  Ann.  Ixv.  p.  504,  1898. 

t  Hon.  R.  J.  Strutt,  Nature,  Ixi.  p.  539,  1900. 

J  Hon.  R.  J.  Strutt,  Phil.  Trans.  A.  196,  p.  507,  1901. 


312  BECQUEREL  RAYS.  [162 

rays  from  polonium  when  they  pass  through  different  gases. 
Rutherford's  results  (see  p.  249)  indicate  that  the  amount  of 
ionisation  would  be  proportional  to  the  coefficient  of  absorption 
of  the  rays  in  the  gas.  Strutt's  results  are  given  in  the  following 
table  (p.  313),  which  for  convenience  of  comparison  contains  the 
relative  ionisation  produced  by  Rontgen  rays  as  determined  by 
Perrin  and  J.  J.  Thomson  and  also  the  relative  ionisation  pro- 
duced by  cathode  rays  as  determined  by  McClennan*. 

162.  Thus  for  the  cathode  rays  and  the  deflectable  Becquerel 
rays,  the  coefficient  of  absorption  depends  only  upon  the  density 
and  not  upon  the  chemical  composition  or  physical  state  of  the 
substances;  the  non-deviable,  easily  absorbable  Becquerel  rays 
approximate  to  this  law  but  deviate  from  it  sensibly  more  than 
the  deflectable  rays,  while  in  the  case  of  the  Rontgen  rays  there 
is  no  approximation  to  this  law.  An  inspection  of  the  result 
shows  that  hydrogen  is  anomalous,  the  ionisation  for  the  deflect- 
able rays  being  very  considerably  greater  than  its  density 
warrants.  The  law  of  absorption  for  those  rays  which  consist 
of  rapidly  moving  negatively  electrified  corpuscles  is  of  great 
interest  in  connection  with  the  theory  of  the  structure  of  matter. 
For  it  is  exactly  the  result  we  should  expect  if  the  molecules  of 
the  different  chemical  elements  consisted  of  differently  arranged 
aggregations  of  a  primordial  atom,  the  number  of  these  atoms  in 
the  molecule  being  proportional  to  the  mass  of  the  molecule, 
i.e.  to  its  molecular  weight ;  then  if  the  corpuscles  forming  the 
cathode  or  deflectable  Becquerel  rays  are  so  small  that  they  can 
thread  their  way  between  the  individual  primordial  atoms  in  the 
molecules  of  the  chemical  elements,  the  collisions  the  corpuscles 
make  when  passing  through  any  body  are  collisions  with  the 
primordial  atoms  in  the  molecule  rather  than  with  the  molecule 
as  a  whole.  Thus  the  mean  free  path  of  a  corpuscle  will  be 
inversely  proportional  to  the  number  of  primordial  atoms  in  unit 
volume ;  this  number  since  all  these  atoms  are  to  be  considered  as 
having  the  same  mass  will  be  proportional  to  the  mass  of  unit 
volume  of  the  substance,  hence  the  mean  free  path  of  the  cor- 
puscles will  be  inversely  proportional  to  the  mass  of  the  substance 
and  will,  if  the  mass  is  kept  constant,  not  be  affected  by  any 
changes  in  its  chemical  composition  or  physical  state.  If  L  is  the 

*  McClennan,  Phil.  Trans.  A.  195,  p.  49,  1901. 


162] 


BECQUEREL   RAYS. 


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314  BECQUEREL   BAYS.  [163 

mean  free  path  of  a  corpuscle  and  if  we  suppose  that  at  each 
collision  the  corpuscle  loses  the  fraction  (3  of  its  kinetic  energy, 
then  X  the  coefficient  of  absorption  =  J3/L,  and  as  L  is  inversely 
proportional  to  the  density  of  the  substance  we  see  that  X  ought 
to  be  proportional  to  the  density,  a  law  which  the  results  we  have 
quoted  show  to  be  very  approximately  true. 

163.  The  penetrating  power  of  the  radium  rays  is  much 
greater  than  that  of  the  cathode  rays  produced  by  electrical  means; 
this  can  readily  be  accounted  for  by  the  greater  velocity  of  the 
corpuscles  in  the  former  rays  if  we  regard  the  collisions  which 
take  place  between  the  corpuscles  and  the  primordial  atom  as 
analogous  to  the  deflection  two  bodies  exerting  forces  on  each 
other  experience  when  they  pass  one  another  at  close  quarters. 
Taking  this  view  of  a  collision  let  us  define  a  collision  as  a  case 
where  the  corpuscle  and  the  primordial  atom  come  so  close 
together  that  the  angle  through  which  the  direction  of  motion 
of  the  path  of  the  former  is  twisted  exceeds  a  certain  value. 
This  deflection  depends  upon  the  initial  velocity  of  the  corpuscle 
and  its  minimum  distance  from  the  atom ;  and  the  theory  of 
central  forces  shows  that  a  collision  will  not  occur  if  the  kinetic 
energy  of  the  corpuscle,  when  so  far  away  from  the  atom  that  the 
force  between  them  is  inappreciable,  exceeds  a  certain  multiple  of 
the  work  done  on  the  corpuscle  by  the  atom  when  the  former 
moves  from  an  infinite  distance  to  its  point  of  nearest  approach 
to  the  atom.  To  take  a  definite  case,  let  us  suppose  that  the 
forces  between  the  corpuscle  and  the  atom  are  electrical  in  their 
origin  and  that  the  charges  on  the  atom  and  corpuscle  are  equal, 
then  if  m  is  the  mass  of  a  corpuscle,  e  its  charge  in  electrostatic 
measure,  v  its  velocity  at  an  infinite  distance  from  the  atom,  d  the 
least  distance  between  the  atom  and  corpuscle;  then  the  work 
done  on  the  corpuscle  is  e*/d  and  the  condition  for  a  collision  is 
that 

02 

-j  should  not  be  less  than 

where  &  is  a  numerical  constant.  Thus  d  cannot  be  greater  than 
2ez/kmv*.  We  may  get  a  rough  idea  of  the  effect  due  to  the 
velocity  if  we  take  'this  value  of  d  as  the  radius  of  the  sphere  of 
action  of  the  atom,  and  suppose  a  collision  to  occur  whenever  a 
corpuscle  passes  through  this  sphere.  Now  the  mean  free  path 


163]  BECQUEREL   RAYS.  315 

varies  inversely  as  the  square  of  the  radius  of  the  sphere  of  action, 
thus  for  this  law  of  force  the  mean  free  path  will  be  directly 
proportional  to  the  fourth  power  of  the  velocity.  The  coefficient 
of  absorption  (which  see  p.  314)  is  equal  to  @/L,  where  L  is  the 
mean  free  path,  hence  neglecting  any  variation  in  /3  the  coefficient 
of  absorption  will  vary  inversely  as  the  fourth  power  of  the  velocity 
of  the  corpuscles :  thus  a  theory  of  this  kind  will  explain  why  the 
penetrating  power  of  the  more  rapidly  moving  corpuscles  in  the 
deflectable  radiation  is  so  much  greater  than  that  of  the  cathode 
rays  in  Lenard's  experiments.  The  essential  condition  for  the 
penetrating  power  of  the  corpuscles  to  be  independent  of  every- 
thing except  the  density  of  the  substances  through  which  they 
are  passing  is  that  the  collisions  which  impede  the  progress  of 
the  corpuscles  should  be  collisions  with  the  individual  primordial 
atoms  and  not  collisions  with  the  molecule  as  a  whole ;  for  this 
condition  to  be  satisfied  it  is  evident  that  the  sphere  of  action  of 
one  primordial  atom  must  not  include  other  atoms,  or  if  D  is  the 
distance  between  two  atoms,  D  must  be  greater  than  2es/kmv*t 
or  v*  must  be  greater  than  2e*/kmD.  If  v2  is  smaller  than  this  we 
cannot  expect  the  simple  law  of  absorption  which  holds  for  the 
very  rapidly  moving  corpuscles  to  apply.  Now  in  electrostatic 
measure  efm.  =  3  x  1017,  e  =  3*4  x  10~10,  and  we  shall  assume  that  D 
is  10~9.  Substituting  these  values  we  see  that  v*  must  be  greater 
than  2  x  1016/&  or  v  greater  than  T4  x  108/&*.  Thus  if  the 
velocity  of  the  corpuscle  falls  below  a  value  somewhere  between 
108  and  107cm./sec.,  we  should  expect  the  law  \/d  =  constant  to 
fail. 

For  velocities  smaller  than  this  the  collisions  made  by  a  cor- 
puscle are  to  be  regarded  as  taking  place  between  the  corpuscle 
and  the  molecule  of  the  substance  rather  than  with  the  constituent 
primordial  atoms  of  the  molecule,  and  when  this  is  the  case  the 
mean  free  path  of  the  corpuscle,  say  in  hydrogen,  will  be  four  times 
that  of  a  molecule  of  hydrogen  at  the  same  pressure :  the  factor  4 
has  to  be  introduced  because  the  size  of  a  corpuscle  is  negligible 
compared  with  that  of  a  molecule,  so  that  the  radius  of  the  sphere 
of  action  in  a  collision  between  a  corpuscle  and  a  molecule  is 
one-half  of  that  between  two  molecules. 

It  is  of  some  interest  to  form  an  estimate  of  the  mean  free 
path  of  a  rapidly  moving  corpuscle,  although  we  are  not  yet  in  a 


316  BECQUEREL  RAYS.  [164 

position  to  evaluate  all  the  constants  that  occur  in  the  expression 
for  the  free  path.  By  the  Kinetic  Theory  of  Gases,  L,  the  mean 
free  path  of  a  particle,  is  given  by  the  equation 

L-     -1- 


where  cr  is  the  radius  of  the  sphere  of  action  in  a  collision,  n  the 
number  of  systems  in  unit  volume  of  the  gas  through  which  the 
particle  is  moving.  Putting  for  cr  the  value  2e2/kmv2,  we  find  for 
the  value  of  L  the  free  path  of  a  corpuscle 

~ 

Let  us  suppose  that  the  gas  through  which  the  corpuscle  is 
moving  is  hydrogen  at  atmospheric  pressure,  and  assume  further 
that  the  mass  of  the  primordial  atom  is  the  same  as  that  of  a 
corpuscle,  then  nm  =  8'5  x  10~5  and  we  get 


since  e  is  measured  in  electrostatic  units  m/e=J10~17,  e=3'4x  lO"10, 
substituting  these  values  we  get 


for  a  velocity   equal   to   that  of  some   of   the  corpuscles  in  the 
radium  rays,  i.e.  2  x  1010,  L  is  equal  to  7&2  centimetres. 

The  influence  of  the  velocity  of  a  corpuscle  on  the  effects  of  a 
collision  is  considered  more  fully  on  p.  344. 

Emanation  from  Radium  and  induced  Radio  -activity 
produced  by  it. 

164.  M.  and  Mme  Curie*  have  shown  that  the  walls  of  a 
vessel  containing  radium  become  radio-active.  Radium,  like 
thorium,  gives  out  an  emanation  which  is  also  radio-active.  The 
persistence  of  the  radio-activity  of  the  emanation  from  radium  is, 
however,  very  much  greater  than  that  from  thorium  :  the  latter, 
as  we  have  seen,  falls  to  half  its  value  in  about  one  minute, 
while  the  activity  of  the  radium  emanation  lasts  for  several 

*  Curie,  Rapports  presentes  au  Congres  International  de  Physique,  iii.  p.  108, 
1900. 


164]  BECQUEREL   RAYS.  317 

hours;  this  has  been  shown  by  Dorn*  and  Rutherford f.  The 
latter  filled  a  cylinder  with  the  emanation  and  observed  the 
saturation  current  from  time  to  time;  after  the  lapse  of  3*5  hours 
the  current  was  1*31  times  its  initial  value,  after  20  hours  the 
current  had  sunk  to  its  initial  value.  On  blowing  out  the  air 
from  the  cylinder  and  refilling  with  air  free  from  the  emanation 
the  current  fell  to  half  its  value,  showing  that  half  the  current 
was  due  to  the  emanation  and  half  to  the  induced  radio-activity 
on  the  walls  of  the  vessel.  Thus,  in  this  experiment,  it  took 
20  hours  for  the  activity  of  the  emanation  to  fall  to  one-half 
of  its  original  value,  a  great  contrast  to  the  1  minute  required 
for  the  same  fall  in  the  thorium  emanation.  On  the  other  hand 
the  radio-activity  induced  on  neighbouring  bodies  by  the  radium 
emanation  dies  away  more  rapidly  than  that  due  to  the  thorium 
emanation.  The  induced  radio-activity  due  to  radium,  like  that 
due  to  thorium,  concentrates  on  negatively  electrified  bodies. 

Rutherford  f  has  shown  that  heating  has  an  enormous  effect 
on  the  issue  of  the  emanation  from  radium.  The  radium  to  be 
heated  was  placed  in  a  platinum  tube,  and  a  constant  current 
of  air  passed  over  the  radium  and  through  a  testing  vat  in  which 
the  saturation  current  was  measured :  this  current  was  due  to 
the  ionisation  of  the  air  in  the  vat  by  the  radiation  from  the 
emanation,  and  also  by  the  radiation  from  the  walls  of  the  vessel 
which  became  radio-active.  On  heating  the  tube  containing  the 
radium  with  a  small  gas  flame,  the  saturation  current  in  the 
vat  was  increased  300  times :  blowing  the  emanation  from  the  vat 
reduced  the  current  to  1/20  of  its  value  when  the  emanation 
was  present,  showing  that  19/20  of  the  ionisation  was  due  to 
the  emanation,  the  remaining  1/20  being  due  to  induced  radio- 
activity on  the  walls  of  the  vat.  The  experiment  was  repeated 
with  a  larger  gas  flame,  when  the  current  in  the  vat  increased  to 
650  times  the  value  when  the  radium  was  cold ;  with  a  still  larger 
flame  the  current  increased  to  1800  times  its  value,  and  when 
the  platinum  tube  was  red-hot  it  increased  to  5000  times  the 
value  when  cold.  Heating  the  tube  to  a  white  heat  produced 
no  further  increase  in  the  current.  Blowing  out  the  emanation 
from  the  vat  when  the  current  was  greatest  reduced  the  current 

*  Dorn,  Abh.  d.  naturf.  Ges.  Halle,  1900. 

t  Rutherford,  Physikalische  Zeitschr.  ii.  p.  429,  1901. 


318  BECQUEREL  RAYS.  [165 

to  one-fourth,  showing  that  three-fourths  of  the  ionisation  was 
due  to  the  emanation  and  one-fourth  to  the  induced  radio-activity. 
The  radium  was  then  allowed  to  cool ;  on  heating  it  to  a  red  heat 
the  next  day  the  current  was  only  increased  65  times,  and  this 
increase  was  maintained  on  subsequent  coolings  and  heatings. 
This  experiment  suggests  that  the  radium  contains  a  radio-active 
gas  which  can  be  driven  out  by  heating,  and  which  ordinarily  sup- 
plies a  part  of  the  emanation.  M.  and  Mme  Curie  (I.e.)  obtained 
from  radium  a  radio-active  gas,  producing  phosphorescence  on 
the  walls  of  the  glass  vessel  in  which  it  was  contained ;  the 
radiation  from  this  gas  was  sufficiently  powerful  to  penetrate 
the  walls  of  the  tube  and  ionise  the  gas  in  the  neighbourhood. 
No  new  lines  were  found  when  the  spectrum  of  the  gas  was 
examined. 

165.  Molecular  Weight  of  the  Emanation  from  Radium.  We 
can  form  some  estimate  as  to  the  molecular  weight  of  the  radium 
emanation  from  the  determination  made  by  Rutherford  and  Miss 
Brooks*  of  its  coefficient  of  diffusion  through  air.  The  measure- 
ments which  have  been  made  of  the  coefficients  of  inter-diffusion 
of  a  large  number  of  simple  gases  have  shown  that  the  coefficient 
of  diffusion  of  one  gas  into  another  is  approximately  inversely 
proportional  to  the  square  root  of  .the  product  of  their  molecular 
weights:  if  then  we  know  the  rate  of  diffusion  of  the  radium 
emanation  through  air  we  can,  by  the  aid  of  the  preceding  rule, 
determine  its  molecular  weight.  , 

The  method  used  by  Rutherford  and  Miss  Brooks  to  determine 
the  coefficient  of  diffusion  through  air  was  as  follows.  A  long 
brass  cylinder  AB,  Fig.  83,  was  divided  into  two  equal  parts 
by  a  smooth  metal  slide  8,  the  ends  of  the  cylinder  were  closed 
by  ebonite  stoppers,  which  supported  the  brass  tubes  a  and  b: 
the  cylinder  was  insulated  and  connected  with  one  pole  of  a 
battery  of  300  volts,  the  other  pole  of  the  battery  was  earthed: 
the  rods  a  and  b  were  connected  with  a  sensitive  electrometer. 
The  cylinder  was  packed  round  with  felt,  so  as  to  keep  the 
temperature  as  constant  as  possible.  To  get  sufficient  emanation 
into  the  cylinder  the  radium  was  slightly  heated,  and  the  ema- 
nation was  carried  by  a  slow  current  of  air  into  the  cylinder. 

*  Rutherford  and  Brooks,  Trans.  Roy.  Soc.  Canada,  vii.  p.  21,  1901. 


165]  BECQUEREL   RAYS.  319 

When  a  sufficient  quantity  of  the  emanation  had  been  obtained 
the  current  was  stopped,  and  the  apparatus  left  to  stand  for 
several  hours:  the  slide  S  was  then  opened  and  the  current 
began  to  diffuse  from  a  to  b.  The  electrical  currents  through 
a  and  b  were  measured  at  regular  intervals.  Initially  there  is  no 
current  in  B,  but  after  opening  the  slide  the  current  in  B  begins 


£UC7 
\ 


PLAT//WM  TUB£ 


Fig.  83. 

to  increase  and  that  in  A  to  decrease :  measurements  were  made 
of  the  currents  at  regular  intervals,  these  currents  (when  corrected 
for  the  part  due  to  the  induced  radio-activity  on  the  electrodes 
and  walls  of  the  vessel)  give  the  amount  of  emanation  present 
in  the  two  cylinders.  From  the  ratio  of  the  amounts  of  the 
emanation  in  the  two  cylinders,  the  coefficient  of  diffusion  K 
through  air  can  be  calculated  from  the  formula 


here  a  is  the  length  of  the  cylinder,  t  the  duration  of  the  ex- 
periment in  seconds,  8l  and  $2  the  amounts  of  the  emanation  in 
the  cylinders  A  and  B  respectively  at  the  end  of  the  experiment. 
The  values  obtained  for  K  varied  between  '08  and  '15.  The 
authors  state  that  the  emanation  given  off  when  the  radium  is 
first  exposed  to  the  air  diffuses  more  rapidly  than  that  given 
off  at  a  later  period.  Applying  the  law  that  the  coefficient  of 
diffusion  of  one  gas  into  another  varies  inversely  as  the  square 
root  of  product  of  the  molecular  weights  of  the  gases,  the  values 
of  K  found  for  radium  would  indicate  a'  molecular  weight  be- 
tween 40  and  100.  This  shows  that  the  emanation  is  not  the 
vapour  of  radium,  as  M.  and  Mme  Curie  have  shown  that  the 
atomic  weight  of  that  substance  is  about  225. 


320  BECQUEREL   RAYS.  [166 

166.  Chemical  Effects  produced  by  Radium*.     Radium  dis- 
colours glass  with  which  it  is  in  contact ;    the  discoloration  seems 
analogous  to  that  which  is  observed  in  the  glass  of  a  discharge 
tube  exhausted  to  a  very  high  vacuum :  it  produces  in  the  chlorides 
of  the  alkali  metals  changes  in  colour  like   those  produced  by 
the  impact  of  cathode  rays  on  these  salts,  it  also  gives  rise  to 
ozone,  a  strong  smell  of  which  is  perceptible  on  opening  a  bottle 
in  which  strong  radium  has  been  kept. 

Polonium. 

167.  Polonium,  discovered  by  M.  and  Mme  Curie*,  is  found 
in  company  with  the  bismuth  extracted  from  pitch-blende  :  they 
obtained  bismuth  richer  and  richer  in  polonium  by  the  following 

methods  of  fractionation : 

» 

1.  Sublimation  of  the  sulphide  in  vacuo.     The  sulphide  of 
polonium  is  much  more  volatile  than  that  of  bismuth. 

2.  Precipitation  of  solutions  in  nitric  acid  by  water.     The 
precipitated  nitrate   is  much   more  active  than  that  remaining 
behind  in  the  solution. 

3.  Precipitation   by  hydrogen    sulphide   from  a   solution  in 
hydrochloric  acid.    The  precipitated  sulphide  is  much  more  active 
than  the  salt  which  remains  behind. 

Polonium  has  not  been  obtained  in  a  pure  enough  state  to 
give  a  spectrum.  As  far  as  is  known  the  radiation  from  it  is 
entirely  of  the  non-deviable  kind:  polonium  does  not  give  out 
negative  corpuscles,  and  its  radiation  is  very  easily  absorbed,  a 
thin  sheet  of  aluminium  being  able  to  stop  it.  The  radiating 
power  of  polonium  is  not  permanent,  it  continually  gets  weaker 
and  weaker.  Mme  Curie f,  who  measured  the  absorption  by  a 
thin  plate  of  aluminium  of  the  radiation  from  polonium  after  it 
had  traversed  a  certain  thickness  of  air,  found  the  very  remarkable 
result  that  the  further  the  polonium  rays  go  through  air  the  more 
easily  are  they  absorbed  by  aluminium. 

The  arrangement  they  used  to  show  this  is  represented  in 
Fig.  84:  PP,  FP'  are  two  metallic  plates  between  which  the 

*  Curie,  Comptes  Rendus,  cxxvii.  p.  175,  1898. 
t  16.  cxxx.  p.  76,  1900. 


167] 


BECQUEREL   RAYS. 


321 


current  produced  by  a  considerable  potential  difference  is  mea- 
sured in  the  usual  way:  the  polonium  is  placed  at  A  and  the  rays 
from  it  go  through  wire-gauze  at  T.  When  the  polonium  is 


BATTERY 


ELECTROMETER 


Fig.  84. 

covered  with  a  thin  layer  of  aluminium  foil  the  absorption  of  the 
rays  increases  with  the  distance  AT,  and  if  a  second  layer  of 
aluminium  foil  is  placed  over  the  polonium  the  absorption  pro- 
duced by  the  second  layer  is  greater  than  that  produced  by  the 
first ;  this  is  the  opposite  to  what  is  observed  with  the  Rontgen 
rays,  but  in  the  Rontgen  rays  we  have  a  mixture  of  rays  of  very 
varying  powers  of  penetration,  and  when  this  is  the  case  the 
first  layer  must  as  we  have  seen  (p.  246)  produce  greater  absorp- 
tion than  the  second.  The  effects  observed  with  polonium  (and 
they  also  occur  as  Mme  Curie  has  shown  with  the  non-deflect- 
able rays  of  radium)  are  those  which  would  be  produced  if  the 
polonium  rays  were  homogeneous  but  became  less  penetrating 
after  passing  through  an  absorbing  medium.  We  should  expect 
rays  which  consist  of  rapidly  moving  negatively  charged  parti- 
cles to  become  more  easily  absorbed  after  passing  through  an 
absorbing  medium,  as  the  velocity  of  the  particles  diminishes  in 
consequence  of  the  absorption,  and  we  have  seen  that  slow  parti- 
cles are  more  absorbed  than  fast  ones.  The  rays  from  polonium 
however  resemble  Rontgen  rather  than  cathode  rays,  as  they  are 
not  deflected  either  by  electric  or  magnetic  forces.  We  shall  see 
reasons  for  thinking  that  these  rays  consist  of  pulses  of  electric 
T.  G.  21 


322  BECQUEREL   RAYS.  [168 

and  magnetic  force,  the  thickness  of  the  pulse  determining  the 
nature  of  the  rays;  thick  pulses  corresponding  to  easily  absorbed 
rays,  thin  ones  to  penetrating  rays.  Thus,  if  the  thickness  of  a 
pulse  increased  as  the  rays  passed  through  an  absorbing  medium 
we  should  get  the  results  observed  by  Mme  Curie.  Now,  if  we 
suppose  that  the  absorption  of  the  rays  is  due  to  the  communica- 
tion of  kinetic  energy  to  charged  ions  struck  by  the  pulse  we 
can  see  that  such  a  thickening  of  the  pulse  would  take  place,  as 
some  of  the  tubes  of  force  in  the  pulse  would  be  temporarily 
attached  to  the  ion;  thus  the  ion  would  tend  to  hold  them  back 
after  the  pulse  passed  on;  the  tubes  would  ultimately  break  away 
from  the  ion,  but  the  result  of  the  temporary  detention  would  be 
a  separation  of  the  tubes  and  a  broadening  of  the  pulse.  If  this 
effect  is  produced  in  air  it  will  evidently  have  the  effect  of  making 
the  intensity  of  the  rays  die  away  very  rapidly  as  they  get  weaker 
and  thus  make  the  appearance  of  measurable  effect  more  abrupt 
than  it  is  in  cases  where  the  ordinary  law  of  absorption  holds :  as 
an  illustration  of  this  point  Mme  Curie  found  that  a  very  slight 
change  in  the  distance  AT  (Fig.  84)  was  sufficient  to  make  the 
current  between  the  plates  increase  from  a  value  too  small  to  be 
measurable  to  one  of  very  considerable  magnitude. 

Actinium. 

168.  Actinium,  which  is  the  name  given  to  a  very  radio-active 
substance  which  accompanies  the  thorium  extracted  from  pitch- 
blende, was  discovered  by  Debierne*;  it  occurs  in  such  minute 
quantities  that  its    investigation  presents  great  difficulties.      It 
seems  to  possess  to  a  very  high  degree  the  power  of  producing 
induced  radio-activity,  in  this  it  resembles  Th  X  (see  p.  291)  and  it 
seems  not  improbable  that  it  may  turn  out  to  be  this  substance. 

Induced  Radio-activity  on  Negatively  Electrified  Bodies  in  Air. 

169.  Elster  and  Geitel'f  have  found  that  a  strongly  negatively 
electrified  body  suspended  in  the  open  air  or  in  a  large  room 
becomes  temporarily  radio-active.    They  showed  that  if  a  body  was 
connected  with  the  negative  terminal  of  a  Wimshurst  machine  for 

*  Debierne,  Comptes  Rendus,  129,  p.  593,  1899 ;  130,  p.  906,  1900. 
f  Elster  and  Geitel,  Physikalische  Zeitschr.  iii.  p.  76,  1901. 


169] 


BECQUEREL  RAYS. 


323 


some  hours,  on  detaching  the  body  from  the  machine  it  was  found 
to  be  radio-active,  ionising  the  air  in  its  neighbourhood  and  affect- 
ing a  photographic  plate.  It  is  necessary  for  the  success  of 
this  experiment  that  a  very  large  volume  of  air  should  be  exposed 
to  the  electric  field,  thus  the  wire  must  be  in  the  open  air  or  in  a 
large  room.  I  was  not  able  to  get  any  induced  radio-activity 
with  the  air  in  the  normal  state  when  the  wire  was  placed  in  a 
closed  vessel  of  about  500  litres  capacity.  The  material  of  which 
the  negatively  electrified  body  is  made  does  not  seem  to  have 
much  effect  upon  the  amount  of  induced  radio-activity,  paper 
giving  as  large  an  effect  as  metal..  A  piece  of  metal  made  radio- 
active in  this  way  can  be  heated  to  redness  without  losing  its 
activity;  if  the  surface  of  the  radio-active  metal  is  dissolved  in  acid 
the  acid  becomes  radio-active ;  this  is  most  conveniently  proved 
by  evaporating  the  acid  to  dryness  and  testing  the  residue.  The 
radio-activity  produced  in  this  way  gradually  dies  away.  Ruther- 
ford and  Allen*,  who  have  measured  the  rate  at  which  it  decays, 

Curve  1.  Induced  radio-activity  from  air. 
Curve  2.  ,,  ,,  ,,      thorium. 

Curve  3.  Thorium  rays. 

Curve  4.  Uranium  rays. 


0123 

Layers  of  tinfoil. 

Fig.  85. 

found  that  the  induced  radio-activity  falls  to  about  half  its  value 

in  three-quarters  of  an  hour ;   the  induced  radio-activity  due  to 

*  Rutherford  and  Allen,  Physikalische  Zeitschr.  iii.  p.  225,  1902. 

21—2 


324  BECQUEREL   RAYS.  [170 

thorium  emanation  is  as  we  have  seen  much  more  persistent  than 
this.  Rutherford  has  also  compared  the  penetrating  power  of  the 
radiation  from  the  negatively  electrified  wire  in  air  with  that  of 
the  rays  from  substances  made  active  by  the  thorium  emanation 
and  with  the  non-deviable  rays  from  thorium  and  uranium ;  the 
results  which  represent  the  proportion  which  pass  through  1,  2,  3, 
4  layers  of  tinfoil  each  3'4  x  10~4  cm.  thick  are  represented  in 
Fig.  85 ;  it  will  be  seen  that  of  the  radiations  tested  that  induced 
in  air  is  the  most  penetrating.  Elster  and  Geitel  ascribe  the 
induced  radio-activity  to  the  deposition  on  the  wire  of  some 
unknown  radio-active  substance  which  is  diffused  through  the 
atmosphere. 

lONISATION   DUE   TO   PHOSPHORUS;    IN    NEWLY   PREPARED   GASES 
AND   IN   AIR   WHICH    HAS   BEEN    IN    CONTACT   WITH    WATER. 

lonisation  due  to  Phosphorus. 

170.  Air  which  has  passed  over  phosphorus  at  not  too  low  a 
temperature  has  the  power  of  discharging  both  positively  and 
negatively  electrified  bodies.  This  was  known  by  Matteucci*, 
it  was  also  studied  by  Naccarif,  and  was  subsequently  indepen- 
dently discovered  by  Shelford  Bid  well  J.  Barus§,  who  has  made 
a  very  extensive  series  of  observations  on  this  phenomenon,  found 
that  air  which  had  been  treated  in  this  way  was  very  active  as 
a  cloud  producer.  If  hydrogen  is  passed  over  phosphorus  it  does 
not  become  a  conductor  of  electricity. 

There  are  two  points  of  view  from  which  we  may  regard  the 
action  of  the  phosphorus  :  the  first  is  that  the  air  in  passing 
over  the  phosphorus  gets  ionised,  and  after  its  escape  from  the 
phosphorus  consists  of  a  mixture  of  positive  and  negative  ions 
uniformly  distributed  through  the  gas ;  in  fact,  that  the  gas  is 
in  much  the  same  condition  as  if  it  had  been  drawn  past  an 
incandescent  metal  whose  temperature  was  high  enough  to  produce 
both  positive  and  negative  ions  at  its  surface.  The  other  view 
is  that  the  air  passing  over  the  phosphorus  carries  off  phosphorus 

*  Matteucci,  Encyclopaedia  Britannica  (1855  edition),  viii.  p.  622. 

t  Naccari,  Atti  della  Scienze  de  Torino,  xxv.  p.  252,  1890. 

J  Bidwell,  Nature,  xlix.  p.  212,  1893. 

§  Barus,  Experiments  with  Ionised  Air,  Washington,  1901. 


170]  BECQUEREL   RAYS.  325 

dust  or  nuclei,  and  that  each  of  these  nuclei  acts  as  a  centre  of 
ionisation,  ionising  the  gas  in  its  immediate  neighbourhood ;  the 
state  of  the  gas  on  this  view  would  be  similar  to  that  of  a  gas 
containing  a  large  number  of  incandescent  metallic  particles, 
each  of  these  particles  being  surrounded  by  an  envelope  of 
conducting  gas.  On  this  view,  when  the  conducting  gas  was 
placed  in  an  electric  field,  the  conduction  would  be  due  to  the 
motion  of  ions  dragged  out  of  the  gas  in  contact  with  the  nuclei 
by  the  electric  force,  while  the  nuclei  themselves  would  not  be 
displaced.  The  evidence  is  hardly  sufficient  to  enable  us  to  decide 
with  certainty  between  these  two  views:  the  second  one,  however, 
seems  to  me  the  more  probable,  for  Barus  found  that  the  rate 
at  which  the  conductivity  died  away  from  the  phosphorised  air 
was  not  increased  by  the  application  of  a  strong  electric  field. 
The  decrease  in  conductivity  seems  consistent  with  the  view 
that  it  arises  from  the  diffusion  of  the  nuclei  to  the  sides  of 
the  vessel,  a  nucleus  ceasing  to  be  active  as  soon  as  it  becomes 
attached  to  the  walls  of  the  vessel.  The  rate  of  decay  of  conduc- 
tivity would  thus  be  proportional  to  the  number  of  nuclei  striking 
the  walls  of  the  vessel  in  one  second ;  in  the  case  of  a  gas  of 
density  p,  and  whose  average  velocity  of  translation  is  v,  this  num- 
ber is  per  unit  area  of  surface  equal  to  ^pv ;  from  measurements 
of  the  rate  at  which  the  phosphorised  gas  lost  its  conductivity 
Barus  concluded  that  the  nuclei  moved  about  like  the  molecules 
of  a  gas,  only  very  much  more  slowly,  the  average  velocity  of 
the  nuclei  being  only  about  3  cm.  per  second.  Another  reason 
for  supposing  that  the  phosphorus  supplies  the  gas  which  has 
passed  over  it  with  nuclei  capable  of  producing  ions  rather  than 
with  ready-made  ions,  is  the  very  considerable  analogy  that  exists 
between  the  behaviour  of  the  phosphorised  air  and  that  of  air 
which  has  passed  through  water ;  the  properties  of  the  latter  we 
shall  consider  in  the  next  paragraph. 

Barus  made  experiments  to  see  if  the  ionising  properties  of 
the  phosphorised  air  could  be  exerted  through  thin  films  of 
various  materials:  the  only  films  which  he  found  to  transmit 
any  appreciable  effect  were  those  made  of  thin  tissue-paper,  and 
here  the  effect  seemed  to  make  its  way  through  the  pores  rather 
than  through  the  material  itself,  as  on  oiling  the  paper  so  as  to 
stop  up  the  pores  the  transmission  ceased. 


326  BECQUEREL   RAYS.  [171 

Conductivity  produced  by  bubbling  air  through  water. 

171.  As  we  have  seen  (Chap.  I.)  air  when  in  its  normal  state 
conducts  electricity  to  a  certain  extent,  the  saturation  current 
through  the  air  in  a  small  closed  vessel  being  proportional  to  the 
mass  of  the  air  contained  in  the  vessel,  the  saturation  current  per 
unit  mass  of  air  showing  but  little  variation  in  samples  of  air  taken 
from  different  places.  I  have  found,  however,  that  air  which  has 
passed  through  tap  water  acquires  and  retains  for  some  time  very 
much  greater  conductivity  than  normal  air.  One  way  in  which 
this  was  proved  was  to  use  as  the  vat  containing  the  air  a  cylin- 
drical gasometer  about  103  cm.  high  and  75  cm.  in  diameter, 
down  the  axis  of  which  was  a  conducting  wire;  the  conductivity 
of  the  air  was  tested  by  measuring  the  saturation  current 
between  this  wire  and  the  walls  of  the  vat.  If  now  the  air  in 
this  vat  was  made  to  bubble  through  water  the  conductivity 
increased  to  a  very  large  extent.  One  way  of  forcing  the  air 
through  water  was  to  pump  the  air  from  the  vat  by  means  of 
a  water  pump  into  a  second  vessel  (the  process  of  pumping  of 
course  making  the  air  bubble  vigorously  through  the  water), 
and  then  force  the  air  back  from  this  vessel  into  the  vat;  when 
this  circulation  had  been  kept  up  for  about  an  hour  it  was  found 
on  stopping  the  circulation  that  the  conductivity  of  the  air  was 
very  much  greater  than  it  was  before.  I  often  found,  for  example, 
that  it  had  increased  30  or  40  times,  and  I  have  no  reason  for 
supposing  that  this  increase  was  any  approach  to  a  limit.  Another 
convenient  way  of  putting  a  gas  into  this  conducting  condition 
is  by  passing  it  through  a  Gouy  sprayer.  When  once  a  gas  has 
got  into  this  condition  it  remains  in  it  for  a  very  considerable 
time;  thus,  for  example,  I  found  that  after  the  lapse  of  several 
days  after  the  passage  of  the  gas  through  water,  the  conductivity 
was  still  many  times  its  value  before  the  bubbling  through  the 
water  had  occurred. 

This  conducting  gas  can  be  transferred  from  one  vessel  to 
another,  it  can  pass  through  plugs  of  glass-wool  without  losing 
its  conductivity,  nor  does  it  lose  this  property  when  passed  over 
wire-gauze  heated  to  a  red  heat  or  through  white-hot  platinum 
tubes  or  over  hot  copper. 

The  conductivity  of  the  gas  is  due  to  the  continued  pro- 


171] 


BECQUEREL   RAYS. 


327 


duction  of  ions  around  some  nuclei  introduced  into  the  gas  by 
its  passage  through  the  water;  it  cannot  be  explained  by  the 
simple  ionisation  of  the  gas  by  this  process,  i.e.  by  a  production 
of  ions  while  the  air  is  bubbling  through  the  water,  this  pro- 
duction ceasing  as  soon  as  the  air  leaves  the  water,  for  if  this 
were  the  cause  of  the  conductivity  the  current  through  the  gas 
would  continue  to  increase  as  the  electromotive  force  was  in- 
creased :  there  would  in  this  case  be  no  '  saturation '  of  the 
current.  If  no  fresh  ions  were  being  produced  the  increase 
of  electric  force  would  at  first  produce  a  continual  increase  in 
the  current,  but  as  the  old  ions  got  used  up  by  the  current, 
and  no  fresh  ones  being  by  hypothesis  produced,  the  current 
would  gradually  decrease.  The  relation  between  the  current 
and  the  potential  difference  is  not  of  this  character,  but,  as 
the  following  numbers  show,  exhibits  all  the  characteristics  of 
conduction  through  a  medium  in  which  ions  are  being  generated 
at  an  approximately  constant  rate ;  the  numbers  in  the  following 
table  are  proportional  to  the  current  passing  between  a  wire 
placed  along  the  axis  of  the  cylindrical  gasometer  in  which  the 
gas  was  contained  and  the  walls  of  the  gasometer,  when  differ- 
ences of  potential,  indicated  by  the  numbers  in  the  first  column  of 
the  table,  were  maintained  between  the  wire  and  the  walls  of  the 
vessel.  It  will  be  noticed  that  for  equal  differences  of  potential, 
the  current  is  greater  when  the  wire  is  the  positive  electrode 
than  when  it  is  the  negative. 


Potential  difference  between 

Current 

the  wire  and  sides  of  the 

vessel  in  volts 

wire  + 

wire  - 

1000 

250 

150 

800 

220 

140 

600 

205 

140 

400 

150 

128 

200 

125 

97 

160 

105 

80 

120 

80 

70 

80 

67 

45 

40 

40 

30 

The  difference  can  be  explained  by  supposing  that  the  negative 
ions  produced  round  the  nuclei  can  be  more  easily  detached  by 


328  BECQUEREL   RAYS.  [172 

the  electric  field  from  its  neighbourhood  than  the  positive  ions; 
this  is  what  we  should  expect  from  the  greater  mobility  of  the 
negative  ions,  part  of  the  positive  ions  may  get  attached  to  the 
nuclei  and  as  these  are  almost  immovable  the  positive  ions  en- 
gaged in  this  way  could  not  take  any  part  in  carrying  the  current. 

The  behaviour  of  the  gas  when  it  contains  the  nuclei  intro- 
duced into  it  by  bubbling  through  water  is  very  analogous  to  that 
of  a  gas  containing  the  emanation  from  thorium  ;  the  ionising 
power  of  the  nuclei  introduced  by  the  water  is  however  much 
more  persistent  than  that  of  the  emanation ;  on  the  other 
hand  the  radiation  from  the  nuclei  is  very  much  less  pene- 
trating than  that  from  the  emanation  :  for  gas  which  had  been 
bubbled  through  water  was  passed  for  6  hours  over  a  photo- 
graphic plate  without  producing  any  effect  upon  it.  No  increase 
in  conductivity  was  found  by  bubbling  air  through  alcohol,  ether, 
or  turpentine.  The  increase  in  conductivity  produced  in  air  by 
the  nuclei  introduced  into  it  by  contact  with  water  may  explain 
the  interesting  result  found  by  Elster  and  Geitel*,  that  the  air  in 
closed  caves  in  which  there  is  no  circulation  has  a  much  higher 
conductivity  than  the  air  in  open  spaces,  for  these  nuclei  might 
slowly  diffuse  from  the  walls  of  the  cave  and  so  increase  the  ionisa- 
tion  in  the  air.  If  the  explanation  given  below  of  the  action  of 
the  nuclei  is  correct,  then  the  increase  in  conductivity  might  be 
produced  by  nuclei  of  many  substances  besides  water;  all  that  is 
required  on  this  explanation  is  that  there  should  be  chemical  action 
between  the  air  and  the  substance  forming  the  nuclei. 

Effects  produced  on  a  negatively  electrified  wire  immersed  in  the 

conducting  gas. 

172.  We  have  seen  (p.  294)  that  a  negatively  electrified  wire 
in  a  gas  containing  the  emanation  from  thorium  acquires  the  power 
of  ionising  the  air  in  its  neighbourhood  and  retains  this  power  for 
a  considerable  time.  Elster  and  Geitel  have  shown  that  the  same 
property  is  acquired  by  a  negatively  electrified  rod  exposed  to  the 
open  air,  or  to  the  air  in  a  large  cave  or  cellar,  the  effect  in  the 
latter  case  being  considerably  greater  than  in  the  open  air.  I 
have  found  that  effects  of  a  similar  character  are  produced  by 

*  Elster  and  Geitel,  Physikalisch^e  Zeitschrift,  iii.  pv76,  1901. 


172]  BECQUEREL    RAYS.  329 

negatively  electrifying  a  wire  in  air  whose  conductivity  has  been 
increased  by  bubbling  it  through  water.  I  first  tested  the  effect 
of  negatively  electrifying  the  central  wire  in  the  cylindrical  gaso- 
meter when  the  gas  in  it  was  in  the  normal  state;  the  wire  was 
connected  to  the  negative  pole  of  a  Wimshurst  machine,  the  other 
terminal  of  which  was  put  to  earth  and  maintained  at  a  potential 
of  about  30000  volts  for  6  hours,  the  outside  of  the  gasometer  was 
kept  connected  with  the  earth ;  in  this  case  no  change  could  be 
detected  in  the  wire,  the  saturation  current  in  the  gasometer  was 
the  same  after  the  electrification  of  the  wire  as  it  had  been  before, 
while  if  the  wire  had  ionised  the  air  around  it  the  saturation  current 
would  have  been  increased;  the  volume  of  air  in  the  vessel,  about 
5  x  105  c.c.,  is  thus  too  small  to  give  the  effect  observed  by  Elster 
and  Geitel  in  the  open  air  and*  in  large  rooms.  I  next  tried  the 
effect  of  largely  increasing  the  current  passing  through  the  gas 
during  the  negative  electrification  of  the  wire ;  this  was  done  by 
exposing  the  air  in  the  gasometer  to  Rontgen  rays  during  the 
whole  of  the  time  the  wire  was  kept  connected  with  the  Wims- 
hurst machine ;  the  rays  make  the  conductivity  of  the  gas  very 
much  greater  than  when  it  is  in  the  normal  state,  and  so  largely 
increase  the  number  of  positive  ions  which  come  up  to  the  nega- 
tively electrified  wire.  In  this  case  after  disconnecting  the  wire 
from  the  Wimshurst  machine  and  stopping  the  rays  the  saturation 
current  was  found  to  have  slightly  increased,  the  increase  being 
from  15  to  20  per  cent.;  that  this  was  due  to  a  change  in  the 
property  of  the  wire  and  not  of  the  gas  in  the  vessel  was  shown 
by  replacing  the  wire  by  one  which  had  not  been  electrified,  when 
the  saturation  current  was  found  to  have  its  normal  value.  The 
ionisation  due  to  the  negatively  electrified  wire  (shown  by  the 
increase  in  the  saturation  current)  gradually  died  away  and  was 
not  perceptible  after  about  45  minutes.  The  experiment  was 
repeated  with  the  wire  connected  with  the  positive  instead  of  the 
negative  terminal  of  the  Wimshurst  machine,  but  in  this  case  not 
the  slightest  increase  in  the  saturation  current  could  be  detected. 
When  the  air  was  made  a  conductor  by  bubbling  it  through 
tap  water  very  much  larger  effects  were  obtained.  To  measure 
these  effects  a  second  vessel  was  used  in  which  the  air  was  kept 
in  its  normal  state,  the  wire  to  be  electrified  was  placed  in  this 
vessel  and  the  saturation  current  through  the  vessel  measured, 
(1)  before  the  wire  had  been  electrified,  (2)  after  the  wire  had 


330  BECQUEREL   RAYS.  [173 

been  placed  in  the  gasometer  containing  the  conducting  air  and 
negatively  electrified :  in  most  cases  the  wire  itself  was  used  as 
one  of  the  electrodes  in  the  second  vessel.  When  the  air  in  the 
gasometer  had  been  got  into  a  highly  conducting  state  by  bubbling 
through  water,  the  wire  to  be  tested  was  placed  in  it  and  nega- 
tively electrified  by  connecting  it  with  the  negative  terminal  of  a 
Wimshurst  machine ;  it  was  found  that  even  with  no  more  than 
half-an-hour's  electrification  the  wire  acquired  strong  ionising 
power.  Thus,  to  give  an  example,  the  saturation  current  in  the 
second  vessel  before  the  wire  was  electrified  (the  wire  being  used 
as  one  of  the  electrodes)  was  15,  after  30  minutes'  negative  elec- 
trification in  the  gasometer  the  saturation  current  rose  to  75,  a 
five- fold  increase.  If  the  wire  was  positively  electrified  when  in 
the  gasometer  the  saturation  current  through  the  second  vessel 
was  increased  but  to  a  very  much  smaller  extent  than  if  it  had 
been  negatively  electrified ;  no  increase  was  produced  if  the  wire 
was  not  electrified.  The  ionising  power  given  to  the  wire  by  its 
negative  electrification  gradually  dies  away  after  the  electrification 
has  ceased ;  the  rate  of  decay  varied  somewhat  in  different  cases, 
it  generally  took  about  40  minutes  for  the  ionisation  to  fall 
to  one-half  its  initial  value.  Though  it  is  convenient  to  use  the 
electrified  wire  as  the  electrode  in  the  second  vessel,  it  is  not 
necessary  to  do  this,  an  increase  in  the  saturation  current  is  pro- 
duced when  the  wire  is  merely  placed  in  the  second  vessel  and 
another  wire  used  as  the  electrode.  The  ionising  power  does  not 
seem  to  depend  much  upon  the  material  of  which  the  negatively 
electrified  body  is  made ;  the  following  experiment  illustrates  this. 
Four  wires,  one  copper,  one  zinc,  one  copper  covered  with  sodium 
amalgam  and  the  other  copper  covered  with  a  layer  of  glycerine 
and  water,  were  metallically  connected  together  and  placed  in 
symmetrical  positions  in  the  gasometer  and  negatively  electrified, 
these  wires  were  then  used  separately  as  electrodes  in  the  second 
vessel  when  they  all  gave  approximately  equal  currents,  much 
larger  than  the  normal  one. 

173.  When  the  wire  has  by  negative  electrification  once  been 
put  in  the  state  in  which  it  ionises  the  surrounding  gas  it  remains 
in  this  state  in  spite  of  very  rough  treatment.  Thus  it  can  be 
washed  with  water  and  then  dried  with  filter-paper  without  losing 
this  property;  it  can  be  heated  to  a  bright  red  heat  without  much 


173]  BECQUEREL   RAYS.  331 

detriment  to  its  ionising  power;  an  amalgamated  wire  was  heated 
until  the  mercury  was  driven  off  and  still  retained  its  activity.  If, 
however,  the  active  wire  is  rubbed  with  emery-paper  so  as  to 
remove  the  outside  layers,  or  if  in  the  case  of  a  wire  covered  with 
a  layer  of  water  the  water  is  wiped  off,  then  the  activity  of  the 
wire  is  destroyed.  The  ionising  power  of  the  wire  corresponds  to 
a  very  easily  absorbed  type  of  radiation,  about  half  the  radiation 
being  absorbed  by  a  layer  of  air  at  atmospheric  pressure  about 
2  cm.  thick,  its  effects  can  be  detected  through  thin  layers  of 
aluminium  foil. 

The  properties  of  the  wire  after  having  been  negatively  elec- 
trified in  the  conducting  gas  are  very  analogous  to  those  possessed 
by  a  wire  after  negative  electrification  in  the  open  air  or  in  air 
containing  an  emanation  ;  the  radio-activity  in  these  cases  has 
usually  been  ascribed  to  some  radio-active  substance  adhering  to 
the  wire.  There  are  indications  that  when  air  bubbles  through 
water  it  carries  away  with  it  a  radio-active  gas  which  can  also 
be  extracted  by  boiling  the  water.  For  I  have  found  that  the 
conductivity  acquired  by  the  air  varies  considerably  with  different 
samples  of  water.  The  conductivity  produced  by  Cambridge  tap 
water  is  very  large,  although  the  deposit  obtained  when  the  water 
is  evaporated  to  dry  ness  is  not  appreciably  radio-active;  with  rain- 
water the  increase  in  conductivity  is  very  small,  it  is  increased 
when  certain  salts  such  as  lead  nitrate  are  dissolved  in  the  water. 
I  have  found  a  small  but  appreciable  increase  in  conductivity  from 
the  water  produced  by  the  combustion  of  coal  gas. 

The  conductivity  is  retained  by  the  air  after  it  has  passed 
through  a  porous  plug.  As  the  radio-active  constituent  can  diffuse 
through  a  porous  plug  it  is  possible  by  measuring  the  rate  of 
diffusion  to  determine  the  density  of  the  emanation.  By  com- 
paring the  rates  at  which  the  emanation  and  carbonic  acid  gas 
diffused  through  the  same  plate  I  found  that  the  density  of  the 
emanation  was  between  5  and  6  times  that  of  carbonic  acid. 

The  following  considerations  indicate  that  certain  changes  in 
the  physical  conditions  might  make  a  body  radio-active  indepen- 
dently of  the  deposition  of  an  intrinsically  radio-active  substance. 
We  have,  when  considering  the  phenomena  of  electrification  by 
incandescent  metals  and  of  photo-electricity,  regarded  a  metal 


332  BECQUEREL   RAYS.  [174 

when  in  its  normal  state  as  being  full  of  negatively  electrified 
corpuscles ;  at  ordinary  temperatures  these  corpuscles  have 
not  sufficient  kinetic  energy  to  enable  them  to  overcome  the 
attraction  of  the  metal  arid  shoot  out  from  the  metal  into  the 
surrounding  gas;  when,  however,  the  kinetic  energy  of  the  corpus- 
cles is  sufficiently  increased,  either  by  raising  the  temperature  of 
the  metal  or  by  the  action  of  ultra-violet  light,  they  escape  into 
the  gas  and  produce  electrical  effects.  Now  in  the  case  of  a 
negatively  electrified  wire  placed  in  a  conducting  gas  a  state  of 
things  will  be  set  up  at  the  surface  of  the  metal  which  will  assist 
the  corpuscles  to  escape  into  the  gas.  For  in  consequence  of  the 
negative  electrification  of  the  wire  positive  ions  travel  up  to  it : 
let  us  suppose  that  some  at  least  of  these  do  not  get  discharged 
but  stick  to  the  wire,  forming  a  layer  of  positive  electrification 
close  to  the  surface  of  the  metal,  the  positive  electrification  will 
induce  negative  on  the  metal  so  that  there  will  be  at  the  surface 
of  the  wire  two  oppositely  electrified  layers  close  together,  the 
negative  layer  on  the  wire,  the  positive  layer  outside ;  there  will 
thus  be  a  very  intense  electric  field,  tending  to  pull  the  negative 
electricity  out  of  the  wire  and  thus  making  the  metal  into  a 
cathode  emitting  cathode  rays ;  if  these  corpuscles  are  moving  with 
sufficient  rapidity  to  ionise  the  gas  through  which  they  pass  the 
gas  around  the  metal  will  be  surrounded  by  positive  and  negative 
ions  and  will  thus  be  able  to  discharge  both  positive  and  nega- 
tive electricity  from  the  wire;  if  the  corpuscles  come  out,  but  with 
so  little  kinetic  energy  that  they  are  not  able  to  ionise  the  mole- 
cules of  the  gas  against  which  they  strike,  then  we  should  expect 
the  wire  to  discharge  negative  electricity  more  easily  than  positive, 
for  the  positive  electricity  in  this  case  would  have  to  be  carried 
by  the  positive  ions  in  the  outer  coating  of  the  double  layer  and 
the  experiments  we  have  described  show  that  this  is  only  detached 
with  great  difficulty. 

174.  The  measurements  made  by  H.  A.  Wilson  (see  p.  190) 
show  that  to  ionise  a  molecule  requires  the  expenditure  of  an 
amount  of  energy  equal  to  the  work  required  to  move  the  charge 
on  an  ion  through  about  2  volts,  hence  we  see  that  to  give  to 
the  corpuscles  from  the  ions  sufficient  energy  to  ionise  the  gas 
through  which  they  pass,  there  must  be  a  difference  of  potential 
between  the  positive  and  the  negative  layers  of  at  least  2  volts. 


175]  BECQUEREL   RAYS.  333 

If  the  potential  difference  between  these  layers  exceeds  this 
value  the  corpuscles  dragged  out  of  the  metal  may  ionise  the 
gas  ;  the  corpuscles  in  the  cathode  rays  in  a  vacuum  tube  acquire 
a  velocity  equivalent  to  that  due  to  a  fall  through  several  hundred 
volts;  hence  their  velocity  will  greatly  exceed  that  of  the  cor- 
puscles extracted  from  the  metal  by^  the  double  layer,  the  latter 
correspond  to  very  slow  and  easily  absorbed  cathode  rays.  If 
these  views  are  correct  it  is  not  necessary  to  suppose  that  all 
cases  of  induced  radio-activity  are  due  to  the  deposit  of  a  radio- 
active substance ;  the  formation  of  a  suitable  double  layer  of 
electrification  at  the  surface  of  any  substance  would  impart  this 
property  to  that  substance. 

175.  The  existence  of  a  double  layer  of  electrification  has  long 
been  recognised  in  certain  cases,  it  is  by  means  of  such  a  layer 
that  the  polarisation  of  the  electrodes  immersed  in  an  electrolyte 
is  usually  explained ;  it  seemed  therefore  of  interest  to  try 
whether  such  electrodes  possessed  any  properties  analogous  to 
tnose  possessed  by  a  wire  which  has  been  negatively  electrified 
in  a  conducting  gas.  Two  platinum  wires  were  immersed  in 
dilute  sulphuric  acid,  and  a  current  of  about  1  ampere  was  sent 
through  the  acid ;  these  wires  were  used  as  electrodes  for  about 
half-an-hour  and  then  taken  out,  dried  with  filter-paper,  and 
then  tested  to  see  whether  any  ionisation  was  produced  by  them 
in  the  air  around  them ;  in  many  cases  considerable  ionisation 
was  found  in  the  air  round  the  wire  which  had  been  used 
as  the  negative  terminal  (the  one  at  which  the  hydrogen 
ions  arrive),  but  in  no  case  was  any  such  effect  observed  near 
the  wire  which  had  been  used  as  the  positive  terminal.  The 
amount  of  ionisation  round  the  wire  used  as  the  negative  terminal 
varied  a  good  deal,  even  when  the  intensity  and  the  duration  of 
the  current  between  the  electrodes  was  kept  the  same,  in  some 
few  cases  it  seemed  to  be  absent  altogether;  when  present  the 
ionising  power  died  away  more  rapidly  than  for  a  wire  which 
had  been  negatively  electrified  in  the  air,  and  was  destroyed  by 
processes  which  hardly  affected  the  wire. 


334  BECQUEREL   RAYS.  [176 


Electrification  produced  by  the  bubbling  of  air  through  water,  the 
splashing  of  drops,  the  liberation  of  gases  by  chemical  action 
or  by  electrolysis. 

176.  The  preceding  experiments  relate  to  the  conductivity 
of  the  gas,  and  show  that  the  process  of  bubbling  through  water 
produces  both  positive  and  negative  ions  in  the  gas ;  the  electrifi- 
cation in  the  gas,  i.e.  the  excess  of  the  number  of  positive  over 
that  of  the  negative  ions,  had  previously  been  the  subject  of 
many  investigations.  Thus  Lord  Kelvin  *  showed  that  air  bubbled 
through  water  carried  with  it  a  negative  charge,  the  amount  of 
this  charge  depending  upon  the  purity  of  the  water,  the  addition 
of  salts  or  acids  to  the  water  diminishing  the  effect,  and  in  some 
cases  reversing  the  sign  of  the  electrification.  The  closely  con- 
nected effect  connected  with  the  splashing  of  drops  had  previously 
been  investigated  by  Lenard  f,  whose  attention  was  called  to 
the  question  by  the  well-known  fact  that  there  is  something 
exceptional  in  the  phenomena  of  atmospheric  electricity  at  the 
foot  of  a  waterfall  when  the  water  falls  upon  the  rocks  and 
breaks  into  spray.  Lenard  found  that  when  a  drop  of  water 
splashes  against  a  plate,  a  positive  charge  goes  to  the  water, 
while  the  surrounding  air  is  negatively  electrified.  The  amount 
of  the  electrification  is  influenced  to  a  remarkable  extent  by  the 
purity  of  the  water ;  thus  Lenard  found  that  while  the  effect 
was  very  marked  with  the  exceptionally  pure  water  at  Heidel- 
berg, it  was  alfnost  insensible  with  the  less  pure  water  at  Bonn. 
He  found  too  that  the  splashing  of  a  weak  solution  of  sodium 
chloride  produced  positive  instead  of  negative  electrification  in 
the  air;  thus  while  the  splashing  of  rain  electrifies  the  air 
negatively,  the  breaking  of  waves  on  the  sea-shore  will  electrify 
it  positively. 

In  some  experiments  that  I  made  on  the  subject^,  I  found 
that  the  effects  produced  by  exceedingly  minute  traces  of  some 
substances  were  exceedingly  large ;  thus,  although  rosaniline  is 
a  very  powerful  colouring  agent,  I  found  that  its  presence  in 

*  Lord  Kelvin,  Proc.  Roy.  Soc.  Ivii.  p.  335,  1894. 

f  Lenard,  Wied.  Ann.  xlvi.  p.  584,  1892. 

t  J.  J.  Thomson,  Phil.  Mag.  v.  37,  p.  341,  1894. 


176]  BECQUEREL   RAYS.  335 

water  could  be  detected  by  the  electrical  effect  before  any  change 
in  the  colour  was  apparent. 

Kosters*  found  that  while  air  bubbled  through  pure  water 
was  negatively  electrified,  the  addition  of  '007  per  cent,  of 
sulphuric  acid  to  the  water  made  the  air  coming  through  electri- 
cally neutral,  while  the  addition  of  more  acid  caused  the  air  to 
be  positively  electrified,  although  the  amount  of  this  was  small 
compared  with  the  negative  electrification  due  to  pure  water. 

The  effect  produced  by  the  addition  of  salts  and  acids  to  the 
water  on  the  electrification  of  air  passing  through,  has  also  been 
investigated  by  Lord  Kelvin,  Maclean,  and  Gait"!". 

The  increased  conductivity  of  air,  produced  by  its  passage 
through  water,  is  not  nearly  so  sensitive  to  impurities  in  the 
water  as  the  charge  carried  away  by  the  air.  Thus  I  could  find 
no  appreciable  difference  in  the  conductivity  when  salt,  rosaniline 
or  methyl  violet  was  added  to  the  water,  although  the  amount 
and  even  the  sign  of  the  charges  carried  away  by  air  passing 
through  the  solution  are  very  different.  Very  different  considera- 
tions are  involved  in  the  case  of  the  conductivity  given  to  air 
by  the  water,  and  the  amount  of  charge  given  to  it  by  splashing 
and  bubbling.  The  former  corresponds  to  a  steady  state  which 
continues  for  hours  and  even  days  after  the  passage  of  the  air 
through  the  water:  the  latter  is  no  doubt  largely  influenced  by 
what  occurs  at  the  instant  when  a  fresh  liquid  surface,  due  either 
to  the  bubbles  forcing  their  way  through  the  liquid  or  by  the 
large  increase  in  area  produced  by  the  splashing  of  a  drop,  is 
exposed  to  the  gas. 

LenardJ  found  that  electrification  was  produced  by  many 
liquids  besides  water  and  aqueous  solutions ;  thus,  mercury  pro- 
duced a  very  large  effect  of  the  same  sign  as  water;  if  mercury 
is  vigorously  shaken  up  in  a  bottle,  and  the  air  drawn  off,  it  is 
found  to  be  strongly  charged  with  negative  electricity ;  turpentine, 
too,  gives  a  large  effect  of  the  opposite  sign  to  that  of  water, 
the  air  being  positively,  the  turpentine  negatively,  electrified. 
The  splashing  of  carbon  bisulphide  also  gives  rise  to  considerable 

*  Kosters,  Wied.  Ann.  Ixix.  p.  12,  1899. 

t  Lord  Kelvin,  Maclean,  and  Gait,  Phil.  Trans.  A.  1898. 

I  Lenard,  Wied.  Ann.  xlvi.  p.  584,  1892. 


336  BECQUEREL   RAYS.  [176 

electrification,  the  sign  of  the  electrification  being  the  same  as 
for  water. 

The  nature  of  the  gas  surrounding  the  liquid  has  also  a  very 
considerable  effect  upon  the  electrification;  thus  Lenard  found 
that  the  electrification  due  to  the  splashing  of  water  surrounded 
by  hydrogen  was  much  less  than  when  the  water  was  surrounded 
by  air ;  using  very  carefully  purified  hydrogen,  I  got  only  a  very 
small  electrification,  and  that  of  the  opposite  sign  to  the  effect 
in  air. 

Electrification  due  to  Chemical  Action. 

In  many  cases  of  chemical  combination  in  which  gases  take 
part  we  get  electrification  of  the  gas;  Pouillet*  was  the  first 
to  discover  an  example  of  this  effect ;  he  found  that  while 
a  carbon  cylinder  is  burning,  the  air  round  the  cylinder  is  posi- 
tively while  the  cylinder  itself  is  negatively  electrified.  Lavoisier 
and  Laplace  f  showed  that  the  same  effect  occurs  with  glowing 
coal.  Pouilletj  also  found  that  when  a  jet  of  hydrogen  burns 
in  air,  there  is  positive  electrification  in  the  surrounding  air, 
negative  electrification  in  the  hydrogen.  Lavoisier  and  Laplace  § 
found  that  when  hydrogen  is  rapidly  liberated  by  the  action  of 
sulphuric  acid  on  iron  there  is  considerable  positive  electrification 
in  the  gas ;  in  this  case  the  interpretation  of  the  results  is  made 
difficult  by  the  electrical  effects  produced  by  the  bubbling  of  the 
gas  through  the  liquid,  these  we  should  expect  to  be  very  con- 
siderable as  the  gas  is  liberated  in  small  bubbles,  which  is  the 
most  favourable  case  for  getting  a  considerable  electrification  in 
a  given  volume  of  air.  This  and  other  cases  of  electrification 
by  chemical  action  have  been  investigated  by  Enright||  and  by 
TownsendV,  the  latter  showed  that  the  hydrogen  produced  by 
the  action  of  sulphuric  acid  on  iron  retained  its  electrification 
after  passing  through  tubes  filled  with  tightly  packed  glass-wool, 
thus  proving  that  the  electrification  could  not  be  carried  by  the 
coarse  spray  produced  by  the  bursting  of  the  bubbles,  as  this  is 

*  Pouillet,  Pogg.  Ann.  ii.  p.  422. 
t  Lavoisier  and  Laplace,  Phil.  Trans.  1782. 
J  Pouillet,  Pogg.  Ann.  ii.  p.  426. 

§  Lavoisier  and  Laplace,  Memoires  de  V Academic  des  Sciences,  1782. 
||  Enright,  Phil.  Mag.  v.  29,  p.  56,  1890. 

II  Townsend,  Proc.  Camb.  Phil.  Soc.  ix.  p.  345,  1898 ;  Phil.  Mag.  v.  45,  p.  125, 
1898. 


176]  BECQUEREL   RAYS.  337 

stopped  by  the  wool.  Townsend  also  showed  that  when  chlorine 
is  liberated  by  the  action  of  hydrochloric  acid  on  manganese 
dioxide  the  chlorine  has  a  strong  positive  electrification ;  and  that 
the  oxygen  produced  by  heating  potassium  permanganate  carries 
with  it  a  strong  positive  charge. 

Townsend  has  shown  that  gases  liberated  by  electrolysis  carry 
with  them  considerable  charges  of  electricity.  Thus  the  hydrogen 
evolved  by  the  electrolysis  of  sulphuric  acid  at  temperatures  as 
high  as  40°  or  50°  C.  has  a  considerable  positive  charge ;  the 
charge  on  the  oxygen  is  exceedingly  small  in  comparison,  it  is  also 
positive.  When  these  gases  are  liberated  by  the  electrolysis  of  a 
solution  of  caustic  potash  the  electrification  on  the  hydrogen  is 
very  small,  while  the  oxygen  has  a  much  larger  negative  charge 
the  amount  of  which  rapidly  increases  with  the  temperature;  the 
nature  of  the  electrode  too  has  a  considerable  influence  on  the 
amount  of  electrification  which  comes  off  in  the  gas.  The  interpre- 
tation of  these  results,  like  those  of  the  evolution  of  gases  by  the 
action  of  acids  on  metals,  is  made  difficult  by  the  electrical  effects 
produced  by  the  bubbling  of  the  gases  through  the  liquid. 
Rosters*,  who  has  also  investigated  this  subject,  ascribes  most  of 
the  electrification  to  the  bubbling. 

Townsendf  found  that  these  electrified  gases  possess  the 
remarkable  property  of  producing  a  cloud  when  they  pass  into 
a  vessel  containing  aqueous  vapour;  this  cloud  is  produced  even 
when  the  air  in  the  vessel  is  far  from  saturated  with  moisture,  and 
does  not  require  any  lowering  of  temperature  such  as  would  be 
produced  by  the  expansion  of  the  air  in  the  vessel.  Townsend 
found  that  when  the  gas  liberated  by  electrolysis  was  not  charged 
no  cloud  was  produced,  and  that  the  weight  of  cloud  produced,  other 
circumstances  being  the  same,  was  proportional  to  the  charge  in 
the  gas.  Clouds  are  produced,  however,  in  some  cases  in  which  .-to 
charges  are  perceptible;  thus  H.  A.  Wilsonj  has  shown  that  if 
solutions  of  salts  or  acids,  or  even  of  sugar  or  glycerine,  are  sprayed 
by  a  Gouy  sprayer  into  a  vessel  and  the  air  from  this  vessel  passed 
through  sulphuric  acid  a  cloud  is  formed  when  this  air  emerges 
into  a  damp  atmosphere.  The  cause  of  this  seems  fairly  clear, 

*  Rosters,  Wied.  Ann.  Ixix.  p.  12,  1899. 

t  Townsend,  Proc.  Comb.  Phil.  Soc.  ix.  p.  345,  1897. 

J  H.  A.  Wilson,  Phil.  Mag.  v.  45,  p.  454,  1898. 

T.  G.  22 


338  BECQUEREL   RAYS.  [177 

although  the  passage  through  the  sulphuric  acid  robs  the  drops  of 
the  solution  of  the  water,  the  acid  or  salt  in  the  drop  is  carried 
along  with  the  air  through  the  sulphuric  acid;  when  this  emerges 
into  the  moist  atmosphere  the  water  condenses  round  the  salt  or 
acid  and  forms  a  drop  of  the  solution,  thus  the  drops  in  the  cloud 
are  not  pure  water,  but  solutions,  and  as  the  vapour  pressure  for 
these  solutions  is  smaller  than  that  for  pure  water  the  drops  do 
not  evaporate,  even  although  the  atmosphere  is  not  saturated  with 
moisture.  Meissner*  has  also  described  clouds  not  accompanied 
by  electrification  which  are  produced  when  air  containing  ozone  is 
passed  through  a  solution  of  potassium  iodide:  these  can  be  ex- 
plained in  a  similar  way  by  supposing  that  the  ozone  acting  on 
the  potassium  iodide  produces  some  substance  which  readily  dis- 
solves in  water  when  it  comes  into  contact  with  it.  I  think  that 
a  similar  explanation  may  hold  for  the  clouds  produced  by  the 
electrified  gas,  for  the  carriers  of  the  electricity  are  evidently 
complex  bodies  of  very  considerable  size,  since  Townsendf*  found 
that  the  velocity  of  these  carriers  under  a  potential  gradient  of 
1  volt  per  cm.  was  only  about  1/8000  of  the  velocity  under  the 
same  electric  field  of  the  ions  produced  by  the  action  of  the  Rontgen 
rays  on  the  gases :  if  we  suppose  that  these  systems  can  dissolve 
in  water  like  an  acid  or  salt  and  lower  the  vapour  pressure,  the 
process  by  which  the  cloud  is  formed  would  be  the  same  as  that 
in  H.  A.  Wilson's  experiment. 

Townsend  measured  the  rate  of  fall,  the  weight  of  the  cloud, 
and  the  amount  of  electrification  carried  by  it ;  the  first  of  these 
measurements  gives  the  size  of  a  drop,  the  second  the  number  of 
drops,  and  the  third  the  charge  on  a  drop ;  he  found,  assuming 
each  drop  to  be  charged,  that  the  magnitude  of  the  charge  on  the 
carrier  of  the  electricity  in  electrolytic  oxygen  was  about  5*1  x  10~10 
electrostatic  units. 

lonisation  produced  by  the  motion  of  negatively  electrified 
corpuscles. 

177.  The  motion  of  negatively  electrified  corpuscles  plays  an 
exceedingly  important  part  in  the  electrical  properties  of  gases ; 

*  Meissner,  Jahresber.  f.  Chem.  1863,  p.  126  ;  see  also  Townsend,  Proc.  Camb. 
Phil.  Soc.  x.  p.  52,  1899. 
t  16.  ix.  p.  345,  1897. 


177]  BECQUEREL   RAYS.  339 

we  have  already  seen  that  it  is  of  fundamental  importance  in  the 
phenomena  connected  with  incandescent  solids  and  with  photo- 
electric effects,  and  we  shall  find  subsequently  that  it  ia  of  equal 
importance  in  the  phenomena  connected  with  sparks  and  dis- 
charges through  vacuum  tubes  where  the  conductivity  of  the  gas 
is  produced  by  the  electric  field  itself:  it  is  therefore  desirable 
to  consider  the  laws  of  ionisation  by  moving  corpuscles  indepen- 
dently of  the  method  of  production  of  the  corpuscles. 

The  fact  that  gas  traversed  by  Lenard  rays  can  discharge 
electrified  bodies  whether  the  electrification  is  positive  or  negative 
shows  that  the  rapidly  moving  corpuscles  constituting  those  rays 
ionise  a  gas  when  they  pass  through  it.  The  ionisation  of  a  gas 
due  to  the  passage  through  it  of  cathode  rays  inside  a  vacuum 
tube  was  shown  by  the  author*  using  the  arrangement  represented 
in  Fig.  86.  A  pencil  of  cathode  rays  from  the  cathode  C  passed 


Fig.  86. 

through  holes  in  two  metal  plugs  connected  with  the  earth  and 
then  between  two  parallel  metal  plates  D,  E ;  one  of  these  plates 
was  connected  with  one  pole  of  a  battery,  the  other  pole  of  which 
was  put  to  earth,  and  the  other  plate  to  one  pair  of  quadrants  of 
an  electrometer,  the  other  pair  of  quadrants  being  to  earth ;  the 
plates  were  so  arranged  that  the  pencil  of  cathode  rays  did  not 
strike  against  either  of  them.  When  the  cathode  rays  were  not 
passing  between  the  plates  there  was  no  appreciable  current  of 
electricity  between  the  plates,  but  when  the  rays  passed  between 
the  plates  the  current  if  the  pressure  of  gas  was  not  too  low 
was  very  appreciable.  The  relation  between  the  current  and  the 
potential  difference  between  the  plates  was  of  the  character  typical 
of  an  ionised  gas ;  the  current  very  soon  reached  a  maximum  value, 
beyond  which  it  did  not  increase  for  a  considerable  range  of  poten- 

*  J.  J.  Thomson,  Phil.  Mag.  v.  44,  p.  293,  1897. 

22—2 


340  BECQUEREL   RAYS.  [178 

tial  difference;  when  the  pressure  was  very  low  the  current  between 
the  plates  got  very  small,  as  now  there  were  very  few  molecules 
for  the  cathode  rays  to  strike  against  and  ionise.  This  and  the 
case  of  the  Lenard  rays  show  that  rapidly  moving  corpuscles  ionise 
the  gas  through  which  they  pass.  Since  it  requires  a  definite 
amount  of  energy  to  ionise  a  molecule  of  a  gas  it  is  evident  that 
ionisation  will  not  occur  unless  the  corpuscles  possess  more  than  a 
certain  amount  of  energy,  i.e.  are  moving  above  a  certain  speed : 
if  we  assume  that  the  work  required  to  ionise  a  gas  is  that  required 
to  move  the  charge  on  an  ion  through  a  potential  difference  of 
2  volts  the  minimum  velocity  which  must  be  possessed  by  a 
corpuscle  before  it  can  ionise  the  molecules  of  a  gas  by  colliding 
against  them  is  about  6*3  x  107cm./sec.  If  any  corpuscles  are 
present  in  a  gas  acted  upon  by  an  electric  field  the  corpuscles  will 
move  under  the  electric  force,  and  if  under  this  force  they  acquire 
a  velocity  greater  than  the  minimum  velocity  required  to  ionise 
the  gas  these  corpuscles  will  produce  fresh  ions,  and  these  again 
will  generate  other  ions,  so  the  gas  will  rapidly  become  a  con- 
ductor. The  velocity  acquired  by  a  corpuscle  in  an  electric  field 
will  depend  not  only  upon  the  intensity  of  the  electric  field  but 
also  upon  the  free  path  of  the  corpuscle;  after  a  collision  the  direc- 
tion of  motion  of  the  corpuscle  will  be  changed,  it  may  be  that  it 
is  reversed,  in  which  case  the  action  of  the  electric  field  after  the 
collision  will  be  to  destroy  the  velocity  communicated  to  the  par- 
ticle by  the  field  before  the  collision  took  place :  these  considera- 
tions show  that  the  maximum  kinetic  energy  communicated  to 
the  corpuscles  will  be  the  work  done  on  the  corpuscle  by  the 
electric  field  when  the  corpuscle  moves  over  a  space  comparable 
with  its  mean  free  path.  Thus  the  kinetic  energy  communicated 
to  a  corpuscle  by  a  given  electric  field  when  the  free  path  is  long, 
i.e.  when  the  pressure  of  the  gas  is  low,  will  be  greater  than  when 
the  free  path  is  short,  i.e.,  when  the  pressure  of  the  gas  is  high;  thus 
it  is  much  easier  to  make  a  gas  a  conductor  by  this  means  when 
the  pressure  is  low  than  when  it  is  high :  these  considerations 
were  first  given  by  the  writer  in  a  paper  read  before  the  Cam- 
bridge Philosophical  Society,  Jan.,  1900. 

178.  The  mathematical  development  of  this  conception  has 
already  been  given  on  page  231 ;  it  is  shown  there  that  in  the 
case  when  the  ions  are  all  moving  parallel  to  the  axis  of  x,  under 


178]  BECQUEREL  RAYS,  341 

an  electric  force  X,  and  when  the  only  source  of  ionisation  in 
the  gas  is  the  negative  corpuscles, 

where  n  is  the  number  of  corpuscles,  u  is  the  velocity  of  a 
corpuscle  parallel  to  the  axis  of  x  and  the  electric  force,  X  the 
mean  free  path  of  the  corpuscle ;  f(Xe\)  the  ratio  of  the  number 
of  cases,  in  which  a  collision  leads  to  ionisation,  to  the  whole 
number  of  collisions ;  7  the  ratio  of  the  number  of  cases,  in  which 
collision  leads  to  the  recombination  of  the  corpuscle,  to  the  whole 
number  of  collisions.  Since  (nu/\)f(Xe\)  is  the  number  of 
fresh  ions  produced  by  the  corpuscles  in  unit  time,  and  as  they 
move  in  this  time  through  ucm.,  f(Xe\)/\  is  the  number  of 
ions  produced  by  a  corpuscle  in  moving  over  1cm.:  denoting 
this  quantity  by  a,  we  get  •* 

d  , 


or  nu=e 

where  G  is  the  value  of  nu  when  x  —  0. 

If  the  field  is  strong  enough  to  make  the  corpuscles  reach 
the  electrodes  before  they  have  time  to  recombine,  7  =  0,  and 
we  have 

nt* 


nu  is  the  quantity  of  negative  electricity  passing  in  unit  time 
through  unit  area  of  a  plane  at  right  angles  to  the  axis  of  X 
at  a  distance  x  from  the  origin,  and  can  be  measured  by  placing 
a  metal  plate  at  this  distance,  connecting  it  with  an  electrometer, 
and  measuring  by  means  of  this  instrument  the  rate  at  which 
negative  electricity  is  reaching  the  plate.  A  very  valuable  series 
of  experiments  on  this  effect  have  been  made  by  Townsend*  and 
Townsend  and  Kirbyf  who  have  determined  the  values  of  a  for 
gases  under  different  pressures  and  for  electric  fields  of  different 
intensities.  The  following  are  the  values  of  a  found  by  Townsend 
for  air: 

*  Townsend,  Phil.  Mag.  vi.  1,  p.  198,  1901. 
t  Townsend  and  Kirby,  ib.  p.  630. 


342 


BECQUEREL  RAYS. 


[178 


X  volts 

Pressure 
•17  mm. 

Pressure 
•38  rnm. 

Pressure 
1-10  mm. 

Pressure 
2'1  mm. 

Pressure 
4*1  mm. 

per  cm. 

a 

a 

a 

a 

a 

20 

•24 

_ 

_ 

_ 

40 

•65 

•34 

— 

— 

— 

80 

1-35 

1-3 

•45 

•13 

— 

120 

1-8 

2-0 

1-1 

•42 

•13 

160 

2-1 

2-8 

2'0 

•9 

•28 

200 

— 

3'4 

2'8 

1-6 

•5 

240 

2-45 

3-8 

4-0 

2-35 

•99 

320 

27 

4'5 

5-5 

4-0 

2'1 

400 

— 

5-0 

6'8 

6-0 

3'6 

480 

3-15 

5-4 

8-0 

7'8 

5-3 

560 

— 

5-8 

9-3 

9'4 

71 

640 

3-25 

6-2 

10-6 

10-8 

8-9 

Thus  we  see  that  for  a  given  value  of  X,  a.  begins  by  increasing 
with  the  pressure,  it  attains  a  maximum  at  a  particular  pressure, 
and  then  diminishes  as  the  pressure  increases  ;  we  see  too  that 
the  larger  the  value  of  X  the  higher  the  pressure  at  which 
a  is  a  maximum.  The  values  given  for  a  at  the  two  lowest 
pressures  show  that,  as  the  force  is  increased,  a  approaches 
a  constant  value. 

These  results  follow  at  once  from  the  value  we  have  obtained 
for  a,  viz. 


If  X  is  constant,  then  at  the  pressure  when  a  is  a  maximum, 

da 


or 


where 


=  0, 

ct/v 

f'(Xe\)Xe    /(ZeX) 

X-\  2  "~         '  *  ' 

/v 


-    d.Xe\    • 
equation  (1)  may  be  written 

Xe\f'(Xe\)=f(Xe\)  ....................  (2). 

This  equation  determines  the  value  of  X  when  a  is  a  maximum  ; 
we  see  from  the  form  of  the  equation  that  the  solution  of  (2) 


is  of  the  form 


Xe\  —  c, 


178]  BECQUEREL   RAYS.  343 

where  c  is  independent  of  both  X  and  X ;  thus  the  value  of  X, 
when  a  is  a  maximum,  is  inversely  proportional  to  X,  and  since 
\  is  inversely  proportional  to  the  pressure,  it  follows  that  the 
pressure  at  which  a  has  its  maximum  value  is  proportional  to  X. 

When  the  electric  field  is  so  strong  that  the  kinetic  energy 
acquired  by  the  corpuscle  between  two  collisions  is  great  enough 
to  make  the  corpuscle  ionise  the  molecule  whenever  it  collides 
with  it,  f(Xe\)  =  1  and  a.  =  1/X, ;  hence  a  becomes  in  strong  fields 
equal  to  the  reciprocal  of  the  mean  free  path,  i.e.  to  the  number 
of  collisions  made  by  the  corpuscle  in  moving  over  1  cm.  Thus, 
from  the  table,  we  may  infer  that  a  corpuscle  makes  about  3'25 
collisions  per  cm.  when  moving  through  air  at  a  pressure  of 
•17  mm.  of  mercury.  Townsend  has  shown  that  the  number  of 
collisions  determined  in  this  way  agree  well  with  the  number  de- 
duced from  the  Kinetic  Theory  of  Gases  for  the  collisions  between 
a  body  of  negligible  size  and  one  of  the  size  of  a  molecule  of  air. 
The  number  of  collisions  made  by  a  corpuscle  moving  through 
air  at  a  pressure  of  1  mm.  of  mercury,  as  determined  by  the 
above  method,  is  about  21.  Townsend  and  Kirby  have  shown 
that  the  numbers  of  collisions  made  by  a  corpuscle  moving 
through  hydrogen  or  carbonic  acid  at  this  pressure  are  respec- 
tively 11 '5  and  29:  these,  again,  agree  well  with  the  values 
deduced  from  the  Kinetic  Theory. 

When  we  are  dealing  with  corpuscles  moving  with  the  velo- 
city of  those  in  the  Lenard  rays,  i.e.  with  velocities  between 
109  and  1010  cm./sec.,  the  number  of  ions  produced  is  much  smaller 
than  those  produced  by  the  comparatively  slow  corpuscles  dealt 
with  in  the  preceding  experiment:  thus,  Durack*  has  sLown 
that  a  corpuscle  moving  with  a  velocity  of  5  x  109  cm./sec.  only 
produces  about  *4  ions  when  moving  through  1  centimetre  of 
air  at  the  pressure  of  1  mm.  of  mercury,  and  with  the  still  more 
rapidly  moving  corpuscles  shot  out  from  radium  the  ionisation  is 
still  smaller.  The  effect  of  velocity  on  the  ionisation  may,  I  think, 
be  explained  by  considerations  of  the  following  kind:  let  us 
suppose  that  the  molecules  of  a  gas  consist  of  a  large  number 
of  smaller  particles,  and  that  each  of  these  repels  the  corpuscle ; 
for  the  sake  of  taking  a  definite  case,  let  us  consider  a  molecule 
as  analogous  to  a  metallic  cage  enclosing  a  large  number  of  nega- 
*  J.  J.  E.  Durack,  Phil.  Mag.  vi.  4,  p.  29,  1902. 


344  BECQUEREL  RAYS.  [178 

tively  electrified  particles,  the  force  due  to  these  outside  the  cage 
being  balanced  by  a  positive  charge  on  the  cage  itself,  equal  in 
magnitude  to  the  sum  of  the  negative  charges  on  the  particles 
inside  the  cage  ;  then  if  a  slowly  moving  corpuscle  were  to 
penetrate  the  cage,  the  repulsions  exerted  on  it  by  the  particles 
would  at  once  drive  it  out  before  it  had  penetrated  an  appreciable 
distance  inside  the  cage  :  thus,  in  this  case,  the  number  of 
collisions  made  by  the  corpuscle  in  its  journey  through  the  gas 
would  be  the  same  as  the  number  it  would  make  if  the  molecules 
of  the  gas  were  hard,  impenetrable,  elastic  solids  ;  we  have  seen 
that  this  hypothesis  agrees  well  with  the  results  of  experiments 
on  slowly  moving  corpuscles.  If,  however,  the  velocity  of  the 
corpuscle  is  very  great,  the  repulsion  of  the  particles  inside  the 
cage  will  not  stop  the  corpuscle  ;  the  corpuscle  will  penetrate 
the  cage,  being  deflected  by  every  particle  it  passes.  The  con- 
ditions of  the  problem  are  now  quite  different  from  those  when 
the  corpuscle  was  moving  so  slowly  that  it  could  not  penetrate 
the  cage  ;  we  proceed  briefly  to  consider  the  collisions  in  this 
case.  The  problem  of  the  collision  between  bodies  repelling  each 
other  with  a  force  varying  inversely  as  the  nth  power  of  the 
distance  has  been  investigated  by  Maxwell*,  who  solved  the 
problem  when  the  two  bodies  were  moving  with  any  velocities. 
We  shall  suppose  that  the  velocity  of  the  particles  is  so  small 
with  respect  to  that  of  the  corpuscle  that  they  may  be  supposed 
to  be  at  rest.  In  this  case,  if  T  is  the  kinetic  energy  of  a  cor- 
puscle, §T  the  change  in  T  due  to  a  collision,  then  Maxwell's 

result  gives 

4JM/2 

-  1 


where  Ml}  M2  are  the  masses  of  the  corpuscl'e  and  the  particle 
respectively,  and  6  is  given  by  the  equation 

-  dx 

2 


-  e  =  r 

I 

Jo 


the  force  between  the  bodies  is  supposed  to  vary  inversely  as  the 
nth  power  of  the  distance  between  them,  and 


*  Maxwell,  Collected  Papers,  Vol.  ii.  p.  26. 


178]  BECQUEREL   RAYS.  345 

where  V  is  the  velocity  of  the  corpuscle  before  collision,  6  the 
length  of  the  perpendicular  let  fall  from  the  particle  on  the  line 
of  flight  of  the  corpuscle  before  collision,  and  K  the  force  at 
unit  distance. 

x  is  the  positive  root  of  the  equation 


(n  -  1)  W 

Let  us  take  the  case  when  the  force  varies  inversely  as  the 
square  of  the  distance,  i.  e.  n  =  2,  then  we  have 


7T          -         lx>  dx 

2~e  = 


A     »   2a 

o  ^/  1  -  a?  -  — 


TT 
=      -  sm 


thus  sin 


\/l+a2      (,   .  62F' 
and  hence  BT  =  —  ,,,    *  ,2. 


r 


Since  T  varies  as  F2  we  see  that  when  F  is  small  ST  will 
increase  with  F  and  will  be  proportional  to  F2,  it  will  reach  a 

maximum  value  when  F2  =  -7-    J^.     —2 ,  while  for  larger  values  of 

F,   ST   will  decrease   as    F  increases   and   will  ultimately  vary 

as  1/F2. 

Now  —  BT  is  the  energy  lost  by  the  corpuscle  and  given  up 
to  the  particle ;  thus  ST  will  measure  the  energy  available  for 
dissociating  the  molecule,  the  ionising  effect  will  therefore  reach  a 
maximum  value  and  will  then  diminish  as  the  velocity  increases. 
When  a  is  large,  6  is  proportional  to  I/a,  i.e.  to  1/F2;  now  20 
is  the  angle  through  which  the  direction  of  motion  is  deflected, 
thus,  for  corpuscles  moving  with  different  speeds,  the  ionisation 
of  the  gas  and  the  diffusion  of  the  corpuscles  will  be  proportional 
to  each  other. 


CHAPTER  XIII. 

SPAEK  DISCHARGE. 

179.  WE  have  hitherto  mainly  been  discussing  cases  in  which 
the  ionisation  was  produced  independently  of  the  electric  field 
acting  upon  the  gas,  we  shall  now  proceed. to  the  consideration  of 
cases  in  which  the  ionisation  is  mainly  due  to  the  action  of  the 
electric  field  itself,  and  when  the  electric  field  before  sending  the 
electric  current  through  the  gas  has  first  to  make  the  gas  a  con- 
ductor. Cases  when  ionisation  is  produced  by  an  electric  field  have 
already  been  considered  on  pp.  2 31  et  seq.,  we  shall  now  consider 
the  most  familiar  case  of  this  kind, — the  electric  spark.  To  take 
as  simple  a  case  of  this  as  possible,  let  us  suppose  that  we  have  two 
large  metal  plates  parallel  to  one  another  and  near  together,  let  the 
plates  be  placed  in  connection  with  a  large  battery  of  cells  or  some 
other  means  of  producing  a  difference  of  potential  between  them ; 
then  if  we  start  with  a  very  small  difference  of  potential  between 
the  plates  the  only  current  which  will  pass  from  one  plate  to  the 
other  will  be  the  very  small  one  due  to  the  spontaneous  ionisation 
of  the  gas  between  the  plates ;  this  current  is  npt  luminous  and  is 
proportional  to  the  distance  between  the  plates,  and  so  by  pushing 
the  plates  near  together  may  be  made  as  small  as  we  please.  On 
measuring  the  potential  difference,  however,  a  stage  is  reached 
when  a  current  accompanied  by  luminosity  passes  between  the 
plates,  and  when  this,  the  sparking  stage,  is  reached  the  potential 
differences  between  the  plates  remain  approximately  constant,  even 
when  the  number  of  cells  in  the  circuit  connecting  the  two  plates 
is  increased.  The  potential  difference  between,  the  plates  when 
the  spark  passes  depends  upon  the  distance  between  the  plates, 
i.e.  the  length  of  the  spark,  and  on  the  nature  and  pressure  of  the 
gas  in  which  the  plates  are  immersed ;  the  investigation  of  the 


180]  SPARK   DISCHARGE.  347 

connection  between  these  quantities  has  occupied  the  attention 
of  many  observers.  Before  we  consider  their  results,  it  will  be 
useful  to  consider  some  properties  of  the  spark  which  have  an 
important  effect  on  the  accuracy  of  such  observations. 

180.  We  shall  call  the  greatest  potential  difference,  which  can 
be  applied  to  the  electrodes  for  an  indefinitely  long  time  without 
causing  the  spark  to  pass,  the  spark  potential  difference.  It  must 
not  be  supposed,  however,  that  whenever  a  potential  difference 
just  greater  than  this  is  applied  to  the  plates  a  spark  always 
passes;  it  frequently  happens  that  if  the  potential  difference  is 
only  applied  for  a  short  time  the  air  between  the  plates  can  sustain 
a  much  greater  difference  of  potential  than  the  spark  potential 
without  a  spark  passing  through  it.  Thus  Faraday*  long  ago 
observed  that  it  takes  a  greater  potential  difference  to  start  the 
first  spark  than  is  required  to  keep  up  the  sparks  when  once  they 
have  been  started,  and  that  the  effect  of  one  spark  in  facilitating 
the  passage  of  its  .successors  does  not  die  away  until  the  gas  has 
rested  for  several  minutes.  I  found  that  if  the  gas  is  dried  with 
extreme  care  it  is  possible  to  get  it  to  stand  without  a  spark  pass- 
ing a  potential  difference  three  or  four  times  as  large  as  that 
which  is  sufficient  to  produce  a  spark  in  less  perfectly  dried  gasf. 
The  dry  gas  seems,  however,  to  be  in  an  unstable  state  as  far  as  its 
electrical  properties  are  concerned,  for  when  once  a  spark  has  been 
forced  through  it  the  potential  difference  between  the  plates  falls 
to  the  value  for  a  moist  gas,  and  the  gas  is  riot  again  able  to 
stand  a  greater  potential  difference  until  it  has  rested  for  several 
minutes ;  this  result  suggests  that  if  we  had  a  perfectly  dry  gas  it 
might  not  be  possible  to  start  a  spark  through  it.  The  gas  would, 
however,  be  in  an  unstable  state,  and  may  be  compared  to  a  super- 
saturated solution  into  which  a  foreign  body  has  to  be  introduced 
before  crystallisation  begins,  though  the  process  once  started  con- 
tinues until  the  solution  ceases  to  be  supersaturated.  Another 
analogy  would  be  a  gas  supersaturated  with  aqueous  vapour, 
when  for  condensation  to  take  place  we  require  the  presence  of 
nuclei  round  which  the  drops  may  condense.  The  tendency  of 
the  gas  to  get  into  this  electrically  unstable  state  is  much  dimi- 
nished by  the  presence  of  moisture,  or  of  gases  from  flames,  sparks, 
i 

*  Faraday,  Experimental  Researches,  §  1417. 
t  J.  J.  Thomson,  Phil.  Mag.  v.  36,  p.  313. 


348  SPARK   DISCHARGE.  [180 

or  arcs,  by  the  illumination  of  the  cathode  by  ultra-violet  light,  or 
by  the  exposure  of  the  spark-gap  to  Rontgen  or  Becquerel  rays,  in 
short  by  any  agent  which  introduces  ions  into  the  field.  War- 
burg* has  made  very  extensive  researches  on  the  effect  produced 
by  several  of  these  agents  on  the  passage  of  sparks ;  the  method 
he  used  consisted  in  measuring  the  interval  between  the  applica- 
tion of  a  potential  difference  greater  than  the  spark  potential  and 
the  passage  of  the  spark  ;  this  interval,  which  may  be  several 
minutes  when  the  potential  only  just  exceeds  the  spark  potential, 
diminishes  as  the  potential  difference  increases,  we  shall  call  it 
the  '  lag '  of  the  spark.  The  amount  of  the  '  lag '  has  an  import- 
ant effect  on  many  phenomena  connected  with  sparks ;  thus  for 
example  if  it  is  great  and  an  induction  coil  or  some  other  machine 
furnishing  a  very  rapidly  changing  potential  be  used  ta  produce 
the  spark,  the  terminals  may  support  for  the  short  time  during 
which  the  electric  field  lasts  a  potential  difference  which  would 
produce  a  spark  if  the  lag  were  short;  in  a  case  like  this  an  agent 
might  make  the  spark  pass  by  diminishing  the  time  of  lag 
even  though  it  had  no  effect  on  the  spark  potential.  A  notable 
instance  of  this  is  the  effect  produced  by  ultra-violet  light  on 
sparks  passing  between  the  terminals  of  an  induction  coil.  Hertzf 
showed  that  the  exposure  of  the  spark-gap  to  such  light  facilitated^ 
the  passage  of  the  spark  ;  E.  Wiedemann  and  EbertJ  showed  that 
if  the  negative  electrode  is  screened  off  from  the  light,  leaving  the 
spark-gap  and  positive  electrode  illuminated,  no  effect  is  produced  ; 
we  have  seen  (Chapter  X.)  that  the  illumination  of  a  negatively 
electrified  body  leads  to  a  discharge  of  negative  ions,  and  that  no 
ions  are  produced  when  the  body  is  positively  electrified.  Swyn- 
gedauw§  found  that  if  the  positive  electrode  was  large  its  illu- 
mination helped  the  spark:  it  is  possible  that  with  large  electrodes 
sufficient  light  may  be  reflected  from  the  positive  to  the  negative 
electrode,  or  to  some  body  in  the  neighbourhood  of  the  positive 
electrode  which  is  negatively  electrified  by  induction,  to  cause  the 
negatively  electrified  body  to  emit  ions. 

*  Warburg,  Sitz.  Akad.  d.  Wissensch.,  Berlin,  xii.  p.  223,  1896 ;  Wied.  Ann.  lix. 
p.  1,  1896;  Ixii.  p.  385,  1897. 

t  Hertz,  Wied.  Ann.  xxxi.  p.  983,  1887. 

t  E.  Wiedemann  and  Ebert,  Wied.  Ann.  xxxiii.  p.  241,  1888. 

§  Swyngedauw,  Rapports  presentes  au  Congres  International  de  Physique,  Paris, 
iii.  p.  164. 


180] 


SPARK   DISCHARGE. 


349 


Wiedemann  and  Ebert  (I.e.)  showed  that  the  nature  of  the 
gas  had  considerable  influence  upon  the  amount  of  the  effect 
produced  by  ultra-violet  light,  the  effect  being  especially  large  in 
carbonic  acid  gas  (the  currents  due  to  photo-electric  effects  in  this 
gas  are  much  larger  than  in  air).  Warburg*  showed  that  the 
chief  effect  of  the  ultra-violet  light  was  to  diminish  the  '  lag '  and 
that  the  effect  on  the  spark  potential  was  comparatively  small. 
This  is  clearly  shown  by  the  figures  given  in  the  following  table, 
taken  from  Warburg's  paper:  the  potential  difference  was  produced 
by  a  battery  of  storage  cells,  and  a  contact  make  and  break  was 
used,  by  means  of  which  the  potential  difference  was  applied  to 
the  air-gap  for  a  short  interval,  in  this  case  '0012  sec.  The  frac- 
tions in  the  table  have  for  their  numerators  the  number  of  times 
a  spark  passed  when  the  potential  difference  was  applied  for  this 
time,  and  for  their  denominators  the  number  of  times  the  potential 
difference  was  applied ;  thus  the  fraction  T°^  indicates  that  the 
spark  never  passed,  and  the  fraction  -{-§•  that  it  always  did  so.  The 
gas  used  in  these  experiments  was  hydrogen  at  a  pressure  of 
11  mm.  of  mercury,  the  spark  potential  was  960  volts  in  daylight, 
1080  in  the  direct  light  from  an  arc  lamp,  and  1260  when  this 
light  had  passed  through  glass.  The  electrodes  were  platinum 
spheres,  7  mm.  in  diameter,  and  the  spark  length  was  4*5  cm. 


Potential  Difference 

8 

3 

o 

§ 

3 

$ 

o 

§ 

s 

o 

o 

o 

1 

in  volts 

OS 

•«*< 

iH 

— 

O» 

8 

OS 

<N 

§ 

3 

3 

§ 

t- 

0 

00 

In  the  dark 

<L 

A 

-Ar 

A 

A 

T7iT 

A 

10 

10 

10 

10 

10 

10 

10 

In  daylight   

-L 

JL 

A 

In      the     arc     light 

10 

Iff 

10 

through  glass  

i8 

}$ 

In  the  arc  light  

1% 

ft 

It  will  be  seen  from  this  table  that  while  in  the  dark  the 
spark  does  not  always  pass  even  when  the  potential  difference 
is  9  times  that  required  to  produce  a  spark  when  the  field  is  con- 
tinuous, in  the  arc  light  a  potential  difference  only  a  little  greater 
than  the  minimum  required  to  produce  a  spark,  always  produces 
a  spark ;  the  table  shows  too  that  daylight  produces  a  very  per- 
ceptible diminution  of  the  '  lag.' 

*  Warburg,  Sitz.  Akad.  der  Wissenschaften,  Berlin,  xii.  p.  223,  1896. 


350  SPARK  DISCHARGE.  [181 

Warburg*  showed  that  the  'lag'  in  a  very  dry  gas  was  much 
longer  than  in  one  containing  a  small  quantity  of  water  vapour; 
the  difficulty  of  starting  the  electric  discharge  in  very  carefully 
dried  gas  has  already  been  alluded  to  (see  p.  347). 

The  importance  of  the  'lag'  in  relation  to  the  mechanism  of 
the  spark  discharge  seems  first  to  have  been  realised  by  Jaumannf, 
who  pointed  out  that  while  it  lasted  some  process  must  be  going 
on  in  the  gas  which  converts  it  from  an  insulator  to  a  conductor. 
During  this  process  no  light  can  be  detected  even  in  the  darkest 
room,  and  both  Jaumann  and  Warburg  failed  to  find  by  direct 
experiments  with  electroscopes  any  indication  of  a  current  passing 
through  the  gas  at  this  stage.  Warburg J,  however,  at  low  pres- 
sures observed  some  effects  which  seem  to  indicate  that  during  the 
lag  there  is  a  current  passing  through  the  gas  although  it  is  too 
'small  to  be  detected  by  an  electroscope  or  to  produce  any  lumi- 
nosity. The  evidence  for  this  is  based  on  the  effect  produced  by 
a  magnet  on  the  discharge  through  a  gas  at  low  pressure ;  a  dis- 
charge is  hindered  by  the  action  of  a  transverse  magnetic  field 
owing  to  the  deflection  of  the  ions  which  carry  the  current ; 
Warburg  showed  that  the  magnetic  field  not  only  hampered 
the  luminous  discharge,  it  also  produced  a  great  increase  in  the 
duration  of  the  'lag,'  he  concluded  from  this  that  during  the  lag 
there  is  a  feeble  current  which  is  essential  for  the  production  of 
the  spark,  and  that  the  magnetic  field  by  hampering  this  current 
prolongs  the  time  which  has  to  elapse  before  the  spark  can  pass. 
Walter  §  by  taking  photographs  of  sparks  on  rapidly  moving 
plates  has  shown  that  a  bright  spark  is  preceded  by  faintly  lumi- 
nous brush  discharges.  We  shall  see  when  we  consider  the  theory 
of  the  spark  discharge  that  the  formation  of  a  preliminary  current 
is  necessary  for  the  production  of  the  spark. 

Effect  of  rapid  variations  in  the  potential  of  the  terminals  on 
the  passage  of  a  spark. 

181.  Jaumann  ||  has  made  some  interesting  experiments  on 
the  effect  on  the  spark  length  of  rapid  changes  in  the  electrical 

*  Warburg,  Wied.  Ann.  Ixii.  p.  385,  1897. 

+  Jaumann,  Ib.  Iv.  p.  656. 

J  Warburg,  Ib.  Ixii.  p.  385. 

§  Walter,  Ib.  Ixvi.  p.  636,  Ixviii.  p.  776. 

H  Jaumann,  Wien.  Sitz.  xcvii.  p.  765,  1888. 


181] 


SPARK   DISCHARGE. 


351 


condition  of  the  electrodes.     The  experiments  are  of  the  following 
type.     The  main  current  from  an  electrical  machine  charged  the 


Fig.  87. 

I 

condenser.  B,  while  the  condenser  C  could  be  charged  through 
the  air  space  F,  G  being  a  small  condenser  whose  capacity  was  only 
55  cm.,  while  B  was  a  battery  of  Leyden  jars  whose  capacity  was 
about  1000  times  that  of  C ;  a  wire  was  connected  to  the  inside 
coating  of  B  and  terminated  about  5  mm.  above  the  plate  E, 
which  was  connected  with  the  earth.  A  glow  discharge  passed 
from  the  wire  to  the  plate,  and  the  difference  of  potential  between 
the  outside  and  inside  coatings  of  the  jars  B  was  constant  and  equal 
to  about  12  electrostatic  units.  When  the  knobs  of  the  air  break 
F  were  suddenly  pushed  together  a  spark  about  5  mm.  in  length 
passed  across  the  air  break  and  in  addition  a  bright  spark  5  mm. 
long  jumped  across  the  air  space  at  e  where  there  was  previously 
only  a  glow.  The  passage  of  the  spark  at  F  put  the  condenser  G 
in  connection  with  B,  and  thus  produced  a  rapid  variation  in  the 
potential  of  the  wire,  and  the  spark  at  E  was  the  result.  From 
experiments  of  this  kind  Jaumann  came  to  the  conclusion  that  if 
V  is  the  potential  difference  between  the  electrodes  the  condition 

dV 

for  sparking  is  that   V  -=-  and  not  V  should  have  a  definite  value, 
dt 

so  that  if  we  could  make  the  potential  difference  vary  with  great 
rapidity  it  might  produce  a  spark  even  though  its  magnitude  were 
much  below  the  sparking  value.  I  cannot  see,  however,  that  the 
experiments  justify  this  conclusion  ;  it  must  be  remembered  that 
when  we  add  on  the  small  condenser  we  start  electrical  vibrations, 


352  SPARK   DISCHARGE.  [182 

and  that  while  these  are  going  on  the  maximum  value  of  the 
potential  in  certain  parts  may  greatly  exceed  the  value  when  the 
vibrations  have  died  away.  Thus,  to  take  a  very  simple  case, 
suppose  A  is  a  very  large  Leyden  jar,  while  B  is  a  very  small  one, 
originally  A  is  charged,  B  is  not,  the  outsides  of  both  are  connected 
with  the  earth  ;  if  the  in  sides  of  A  and  B  are  suddenly  connected, 
then  though  the  final  potential  of  B  will  be  smaller  than  the 
initial  value  of  the  potential  of  A,  yet  the  maximum  value  during 
the  oscillations  will  be  nearly  twice  as  large  as  the  initial  poten- 
tial of  A,  and  thus  if  B  were  suddenly  connected  with  A  a  spark 
might  pass  across  the  plates  of  B  although  B  might  stand  without 
sparking  a  potential  difference  equal  to  that  originally  existing 
between  A  :  the  passage  of  this  spark  would,  however,  be  due  to 
the  oscillation  producing  a  great  increase  in  the  maximum  poten- 
tial difference,  and  would  not  necessarily  indicate  that  with  a  given 
potential  difference  the  spark  would  pass  more  easily  if  this  were 
changing  than  if  it  were  steady.  This  question  has  been  the 
subject  of  much  controversy,  it  is  often  called  the  question  of 
'constant  spark  potential'  and  has  been  discussed  by  Jaumann*, 
Swyngedauwf,  and  K.  R.  Johnson  J. 

Variation  of  the  spark  potential  difference  with  the  spark  length 
and  pressure  of  the  gas. 

182.  The  first  measurements  of  the  potential  difference  re- 
quired to  produce  a  spark  through  air  at  atmospheric  pressure  were 
made  by  Lord  Kelvin  §  in  1860,  since  then  the  subject  has  attracted 
much  attention  and  important  investigations  have  been  made  by 
Baille||,  LiebigH,  Paschen**,  Peaceft>  Orglerft,  Struttg,  Bouty||||, 
EarhartlfH  and  Carr***.  The  values  of  the  spark  potential  differ- 

*  Jaumann,  Wied.  Ann.  Iv.  p.  656,  1895 ;   Wien.  Sitz.  xcvii.  p.  765,  1888. 

f  Swyngedauw,  These  :  Contribution  a  VEtude  des  Decharges,  1897. 

J  Johnson,  Drude's  Ann.  iii.  p.  460,  1900 ;  v.  p.  121,  1901. 

§  Lord  Kelvin,  Collected  Papers  on  Electrostatics  and  Magnetism,  p.  247. 

||  Bailie,  Annales  de  Chimie  et  de  Physique  [5],  xxv.  p.  486,  1882. 

IT  Liebig,  Phil.  Mag.  v.  24,  p.  106,  1887. 
**  Paschen,  Wied.  Ann.  xxxvii.  p.  79,  1889. 
ft  Peace,  Proc.  Roy.  Soc.  Iii.  p.  99,  1892. 
$$  Orgler,  Drudc's  Ann.  i.  p.  159,  1900. 

§§  Strutt,  Phil.  Trans.  193,  p.  377,  1900. 
||  ||  Bouty,  Comptes  Rendus,  131,  pp.  469,  503,  1900. 
HIT  Earhart,  Phil.  Mag.  vi.  1,  p.  147,  1901. 
***  Carr,  Proc.  Roy.  Soc.  Ixxi.  p.  374,  1903. 


182]  SPARK  DISCHARGE.  353 

ence  given  by  the  earlier  experimenters  are  as  a  rule  somewhat 
larger  than  those  found  under  similar  circumstances  by  more 
recent  observers,  probably  because  latterly  more  attention  has  been 
paid  to  eliminating  the  effects  due  to  'lag';  whenever  'lag'  is 
present  the  potential  difference  when  the  spark  passes  is  higher 
than  the  minimum  required  to  produce  a  spark.  We  shall  first 
give  a  general  account  of  the  laws  which  have  been  brought  to 
light  by  the  experiments  made  on  this  subject,  reserving  until  the 
end  of  the  chapter  the  tables  which  embody  the  numerical  results 
obtained  by  the  above-mentioned  physicists. 

Let  us  first  take  the  case  where  the  electrodes  are  so  large 
compared  with  the  distance  between  them  and  placed  in  such  a 
position  that  the  lines  of  electric  force  are  parallel  to  each  other, 
this  condition  would  be  fulfilled  if  the  electrodes  were  parallel 
planes  placed  at  a  distance  from  each  other  not  greater  than  a 
small  fraction  of  their  diameter;  it  is  approximately  fulfilled  in 
the  arrangement  most  frequently  used  where  the  electrodes  are 
portions  of  spheres  of  large  radius  placed  close  together. 

In  the  first  place  the  potential  difference  required  to  produce 
a  spark  of  given  length  does  not  aepend  upon  the  metal  of  which 
the  electrodes  are  made  (it  is  possible  that  aluminium  and  magne- 
sium electrodes  may  be  exceptions  to  this  rule).  Experiments 
on  this  point  have  been  made  by  Righi*,  Peace,  and  Carr.  Righi 
tried  electrodes  of  carbon,  bismuth,  tin,  lead,  zinc,  and  copper  and  r 
got  the  same  potential  difference  with  all  these  substances.  Peace 
(I.e.)  who  made  very  careful  experiments  with  electrodes  of  zinc 
and  brass  could  not  detect  the  slightest  difference  in  the 
potential  difference  required  to  spark  across  them.  Carr  found 
the  spark  potential  to  be  the  same  with  electrodes  of  brass,  iron, 
zinc,  and  aluminium.  On  the  other  hand,  De  la  Rue  and  Hugo 
Miillerj-  came  to  the  conclusion  that  sparks  pass  more  easily 
between  aluminium  electrodes  than  between  electrodes  of  any 
other  metal,  but  that  with  this  exception  the  nature  of  the  elec- 
trodes has  no  influence  upon  the  spark  length.  It  is  worthy  of 
remark  that  the  cathode  fall  of  potential  which  is  very  closely  con- 
nected with  the  spark  potential  is  nearly  the  same  for  electrodes 

** 

*  Righi,  Nuovo  Cimento  (2),  xvi.  p.  97,  1876. 

t  De  la  Rue  and  Miiller,  Phil.  Trans.  169,  Pt.  1,  p.  93,  1898. 

T.  G.  23 


354  SPARK   DISCHARGE.  [182 

of  all  the  metals  used  by  Righi ;  for  aluminium  and  magnesium 
electrodes,  however,  it  is  decidedly  smaller. 

The  connection  between  the  spark  potential  and  the  spark 


COAL  GAS. 


100       200       300      *oo       500      coo       700      800       900       iooo  Centimeters 

length  is  represented  by  the  curves  given  in  Figs.  88,  89,  90, 
and    91   for   air,  hydrogen,  and   carbonic  acid   and    coal   gas  at 


AIR. 


100        200       soo       400       500       600        700       800       900      iooo  C 'e utitncfcrs 
Fig.  89. 

atmospheric    pressure,   the    ordinates    are    proportional    to    the 


182] 


SPARK   DISCHARGE. 


355 


potential  difference  required  to  produce  a  spark  of  a  length  repre- 
sented by  the  abscissae. 

The  curves  in   Figs.  88 — 91    are   due  to   Liebig  (I.  c.),  who 
used    spherical   electrodes   19*5  cm.   in   diameter.      The    curves 


HYDROGEN. 


100  2OO  300          400          500          600          700 


800       900       1000  Centime.te.rs 


Fig.  90. 


running  up  to  the  vertical  axes  represent  the  connection  between 
the  average  value  of  the  electric  intensity,  i.e.  V/d  where  V  is  the 
spark  potential  and  d  the  spark  length,  and  the  spark  length. 


100  200  300          400  50 


0  600          700  800  900         1000 


Fig.  91. 

It  will  be  seen  that  except  for  very  short  sparks  the  curves 
representing  the  relation  between   V  and  d  are  approximately 

23—2 


356  SPARK   DISCHARGE.  [183 

straight  lines,  so  that   for  moderately  long  sparks   the  relation 
between  F  and  d  would  be  of  the  form 


where  a  and  b  are   constants.     Chrystal*  has  shown  that  the 
simple  relation 

F=  4-997  +  9 


where  F  is  measured  in  electrostatic  units  and  d  in  centimetres 
agrees  with  Bailie's  very  numerous  experiments  on  the  spark  poten- 
tial in  air  at  atmospheric  pressure  quite  as  well  if  the  spark  length 
exceeds  2  mm.  as  the  more  complicated  formula 

F2=  10500  (d  +  0*08)  d 

proposed  by  Bailie  himself.  Carey  Foster  and  Prysonf  also 
found  that  the  linear  relation  V=a  +  bd  was  the  one  which  best 
represented  the  results  of  their  experiments  on  the  potential 
difference  required  to  spark  through  gas  at  atmospheric  pressure. 

183.  The  curves  we  have  given  do  not  however  give  any  indica- 
tion of  the  relation  between  the  spark  potential  and  the  spark 
length  when  the  latter  is  exceedingly  small.  When  the  spark  length 
falls  below  a  certain  value  which  is  inversely  proportional  to  the 
pressure,  and  which  we  shall  call  the  critical  spark  length,  the 
potential  difference  has  a  minimum  value,  and  if  the  spark  length  is 
still  further  diminished  the  spark  potential  begins  to  increase  and 
goes  on  increasing  until  the  spark  length  gets  down  to  about  10~4cm., 
when  it  very  rapidly  diminishes.  The  increase  of  the  spark  poten- 
tial due  to  a  diminution  in  the  spark  length  was  first  observed  by 
Peace  ;  as  the  critical  spark  length  at  atmospheric  pressure  is 
exceedingly  small,  only  about  '01  mm.,  it  is  difficult  to  experiment 
with  sparks  short  enough  to  show  the  effect,  as  however  the 
critical  spark  length  varies  inversely  as  the  pressure,  we  can  by 
diminishing  the  pressure  increase  the  critical  spark  length  until  its 
observation  becomes  comparatively  easy.  Perhaps  the  simplest  way 
of  showing  the  effect  is  to  use  slightly  curved  electrodes  and  to 
observe  'the  position  of  the  spark  as  these  are  brought  closer 
together.  When  the  electrodes  are  at  some  distance  apart  the 
spark  passes  along  the  shortest  line  between  them;  as  the  electrodes 

*  Chrystal,  Proc.  Eoy.  Soc.  Edin.  xi.  p.  487,  1882. 

t  Catey  Foster  and  Pryson,  Chemical  News,  xlix.  p.  114,  1884. 


183] 


SPARK    DISCHARGE. 


357 


are  pushed  together  it  will  be  found  that  a  stage  is  reached  when 
the  spark  no  longer  passes  along  the  shortest  line,  but  goes  to 
one  side,  taking  a  longer  path,  showing  that  it  is  easier  to  pro- 
duce a  long  spark  than  a  short  one ;  with  this  arrangement  the 
potential  difference  required  to  produce  the  spark  does  not  vary, 
as  the  electrodes  are  moved  nearer  together  it  remains  constant 
and  equal  to  the  minimum  potential  difference  required  to  pro- 
duce a  spark ;  the  spark  length  too  is  constant  and  equal  to  the 
critical  spark  length ;  the  position  of  the  spark  is  determined  by 
the  condition  that  it.  passes  at  the  place  where  the  distance  be- 
tween the  electrodes  is  equal  to  the  critical  spark  length.  In  order 
to  measure  the  increase  of  potential  difference  due  to  the  dimi- 
nution in  spark  length  it  is  necessary  to  use  perfectly  flat  and 
parallel  electrodes,  when  these  are  pushed  together  the  length  of 
the  spark  is  necessarily  diminished.  ,  The  electrodes  used  by  Carr 
(I.  c.)  are  represented  in  Fig.  92 ;  they  were  plane  brass  plates  em- 
bedded in  ebonite  and  separated  by  ebonite  rings  of  different 


-- 


ToBofcry 


thicknesses.     With  this  apparatus  Carr  obtained  the  results  given 
in  the  following  table  : 

Pressure  2'02  mm. :  gas — air. 


Spark  length 

Spark  potential 

in  volts 

1  rnm. 

558 

2  mm. 

371 

3  mm. 

357 

5  mm. 

376 

10  mm. 

472 

• 

358 


SPARK   DISCHARGE. 
Pressure  T05  mm.:  gas — air. 


[183 


Spark  length 

Spark  potential 

in  volts 

1  mm. 

1826 

2  mm. 

594 

3  mm. 

397 

5  mm. 

355 

10  mm. 

37£ 

The  effect  is  even  more  strongly  marked  in  hydrogen,  as  the 
following  table  shows. 

Pressure  2*6  mm.:  gas — hydrogen. 


Spark  length 

Spark  potential 

in  volts 

1  mm. 

1781 

2  mm. 

462 

3  mm. 

398 

5  mm. 

285 

10  mm. 

317 

In  each  of  these  cases  the  spark  potential  for  the  shortest 
spark  is  greater  than  for  the  longest.  When  the  spark  length 
falls  below  about  5  x  10~4  cm.  the  spark  potential,  as  Earhart  has 
shown,  falls  off  rapidly;  we  shall  return  to  this  point  later  on.  The 
existence  of  a  critical  spark  length  is  also  proved  by  the  remark- 
able changes  which  take  place  in  the  appearance  of  the  discharge 
when  the  electrodes  are  brought  very  near  together.  Thus  in  the 
course  of  some  experiments  on  the  discharge  between  large  parallel 
plates  I  observed*  that  at  very  low  pressures  the  discharge  went 
from  the  under  side  of  the  lower  plate,  which  was  the  positive  elec- 
trode, and  round  to  the  top  of  the  upper  plate,  the  space  between 
the  plates  was  quite  free  from  any  luminous  discharge :  showing 
the  discharge  went  more  easily  round  the  longer  path  than  by  the 
much  shorter  one  between  the  plates.  The  same  thing  is  shown 
in  Figs.  93  and  94,  which  are  drawings  given  by  Lehmann'f*  of 
the  appearance  as  seen  through  a  microscope  of  the  discharge 


*  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  v.  p.  395,  1886. 
f  Lehmann,  Moleciilare  Physik,  ii.  p.  295. 


18*] 


SPARK   DISCHARGE. 


359 


between  electrodes  of  different  shapes  placed  very  near  together. 
A  very  famous  experiment  due  to  Hittorf*,  represented  in  Fig.  95, 


Fig.  93. 


Fig.  94. 


is  another  illustration  of  this.    The  two  electrodes  were  only  1  mm. 
apart,  the  regions  around  them  were  connected  together  by  a  long 


Fig.  95. 

spiral  tube  375  cm.  long;  in  spite  of  the  enormous  difference  be- 
tween the  lengths  of  the  paths  the  discharge,  when  the  pressure 
was  very  low,  all  went  round  through  the  spiral,  the  space  between 
the  electrodes  remaining  quite  dark. 

184.     The  curves   in   Figs.    88 — 91    show   how    rapidly  the 
value  of  V/d   (V  being  the  spark  potential  and  d  the  distance 


Hittorf,  Wied.  Ann.  xxi.  p.  96,  1884. 


360 


SPARK   DISCHARGE. 


[185 


between  the  plates)  increases  as  d  diminishes.  This  was  observed 
by  Lord  Kelvin  in  1860.  If  the  electric  field  were  uniform  V/d 
would  be  the  electric  intensity  between  the  plates;  in  general, 
however,  when  a  current  of  electricity  passes  through  a  gas  the 
field  is  not  uniform  but  is  greater  at  one  or  both  of  the  electrodes 
than  in  the  rest  of  the  field,  we  are  not  justified  therefore  in 
assuming  that  V/d  is  the  maximum  electric  intensity  between 
the  electrodes. 


Variation  of  the  spark  potential  with  the  pressure. 

185.  If  the  spark  length  is  constant  and  not  too  small  then, 
starting  with  air  at  atmospheric  pressure,  as  the  pressure  is 
diminished  the  spark  potential  decreases,  the  relation  between  the 
potential  and  pressure  being  at  first  a  linear  one  ;  on  further  diminu- 
tion of  the  pressure  the  spark  potential  reaches  a  minimum  valuer 
after  this  any  further  diminution  in  the  pressure  is  accompanied  by 
an  increase  in  the  spark  potential.  The  relation  between  the  spark 
potential  and  the  pressure  is  represented  by  the  curve  in  Fig.  96, 


Pressure  in  Millimetres 
Fig.  96. 


taken  from  a  paper  by  Carr  (I.e.);  in  this  curve  the  ordinates 
represent  the  spark  potential,  the  abscissae,  the   pressure ;   the 


185] 


SPARK   DISCHARGE. 


361 


electrodes  were  parallel  planes  and  the  spark  length  3  mm.     The 
pressure  at  which  the  spark  potential  is  a  minimum  is  called  the 
critical  pressure.     Peace  (I.e.)  showed  that  the  critical  pressure 
depended  upon  the  spark  length,  the  shorter  the  spark  length  the 
greater  the  critical  pressure.     He  showed  too  that  the  minimum 
spark  potential   was   constant,  being  independent  of  the  spark 
length ;  in  air  it  was  equal  to  about  351  volts,  so  that  unless  thej 
spark  length  is  less  than  about  5  x  10~4  cm.,  a  potential  difference) 
of  less  than  351  volts  cannot  produce  a  spark. 

These  points  are  well  illustrated  by  the  curves  in  Fig.  97,  taken 
from  Carr's  paper;  they  represent  the  relation  between  the  pres- 
sure and  the  spark  potential,  for  sparks  of  1,  2,  3,  5,  and  10  mm. 


/  2  J 

Pressure  in  Millimetres  of  Mercury 
Fig.  97.    Air. 

The  critical  pressures  for  these  spark  lengths  as  given  by  Carr  are 
as  follows. 


Spark  length 

Critical  pressure 

Product  of  spark  length 
and  critical  pressure 

1  mm. 

4-98  mm. 

4-98 

2  mm. 

2'71  mm. 

5-42 

3  mm. 

1-89  mm. 

5-67 

5  mm. 

1-34  mm. 

6'7 

10  mm. 

•679  mm. 

6-79 

362 


SPARK    DISCHARGE. 


[185 


It  will  be  seen  that  the  product  of  the  critical  pressure  and 
the  spark  length  is  approximately  constant:  we  must  remember 
that  owing  to  the  flatness  of  the  curves  in  the  neighbourhood  of 
the  critical  pressure  the  exact  determination  of  the  critical  pres- 
sure is  a  matter  of  some  difficulty,  especially  with  the  shorter 


•tr  -$-&"  D 


400     480      StO      610      720      800 

Pressure  in  Millimetres 
Fig.  98.     Air. 


1040     U20      1200 


Pressure  in  Millimetres 

Fig.  99.     Hydrogen. 

sparks :  the  differences  in  the  product  of  the  critical  pressure  and 
the  spark  length  are  not  greater  than  could  be  accounted  for  by 
the  errors  in  the  determination  of  the  critical  pressure. 

The  same  features  are  shown  by  sparks  through  hydrogen  and 


185]  SPARK  DISCHARGE.  363 

carbonic  acid;  the  curves  for  these  as  given  by  Carr  are  shown  in 


/  2  3  4  S" 

Pressure  in  Millimetres 
Fig.  100.     Carbon  Dioxide. 

Figs.  99  and  100,  and  the  connection  between  the  critical  pressure 
and  the  spark  length  shown  in  the  following  tables: 

Hydrogen.     Minimum  potential  280  volts. 


Spark  length 

0 
Critical  pressure 

Product  of  spark  length 
and  critical  pressure 

1  mm. 

10-3    mm. 

10-3 

2  mm. 

5-93  mm. 

11-8 

3  mm. 

4-02  mm. 

12-06 

5  mm. 

2-8    mm. 

14-0 

10  mm. 

1'46  mm. 

14-6 

Carbonic  acid.     Minimum  potential  420  volts. 


Spark  length 

Critical  pressure 

Product  of  spark  length 
and  critical  ^pressure 

1  rnm. 

5-02  mm. 

5-02 

2  mm. 

2*52  mm. 

5-04 

3  mm. 

1-63  mm. 

4-89 

5  rnm. 

1-07  mm. 

5-35 

10  mm. 

•510mm. 

5-1 

364 


SPARK   DISCHARGE. 


[185 


/     The  constancy  of  the   product   of  spark  length  and  critical 
/pressure  in  the  case  of  carbonic  acid  is  very  marked. 

Carr  has  also  given  curves  for  the  connection  between  spark 
length  and  pressure  for  H2S,  SO2,  CO2,  C2H2,  O2,  N2O ;  these  are 
shown  in  Fig.  101. 


2-2      2-4      26       2-8 


_.__/•        1-2       /-+      1-6       1-8        Z 

Pressure  in  Millimetres 
Fig.  101. 

The  spark  length  for  these  gases  was  3  mm. 

Very  careful  experiments  on  the  relation  between  the  pressure 
and  the  spark  potential  were  made  by  Strutt*  for  air,  hydrogen, 
nitrogen,  and  helium ;  the  experiments  on  nitrogen  and  helium  are 
especially  interesting,  as  the  minimum  spark  potential  in  these 
gases  was  found  by  him  to  be  greatly  affected  by  minute  traces 
of  impurity.  Thus  the  presence  of  a  very  minute  quantity  of 
oxygen  in  nitrogen  increased  the  minimum  spark  potential  from 
251  volts  to  388  volts.  Thus  nitrogen  from  which  the  oxygen  had 
been  removed  by  passing  the  gas  over  metallic  copper  gave  a 
minimum  spark  potential  of  388  volts,  the  value  of  this  potential 
for  a  specjmen  of  nitrogen  prepared  from  air  by  the  absorption  of 
the  oxygen  by  alkaline  pyrogallol  was  347  volts ;  when,  however, 
the  oxygen  was  more  completely  removed  by  bubbling  the  gas 
repeatedly  through  the  liquid  alloy  of  sodium  and  potassium  the 
minimum  spark  potential  fell  to  251.  The  curves  obtained  by 

*  Hon.  R.  J.  Strutt,  Phil.  Trans.  193,  p.  377,  1900. 


185] 


SPARK   DISCHARGE. 


365 


Strutt  for  nitrogen  are  shown  in  Fig.  102.     Curve  No.  2  refers  to 
the  purest  specimen,  curve  No.  1  to  a  specimen  which  had  been 


_t«      600 

•3 

~      500 


I 

£       4°° 

| 

OQ*     300 


0  10  20  30  40  60  60  70  80 

Pressure  in  Millimetres  of  Mercury 
Fig.  102.     Nitrogen. 

passed  several  times  through  the  sodium  and  potassium  alloy,  but 
not  so  often  as  that  to  which  curve  No.  2  relates :  the  minimum 
spark  potential  for  this  specimen  was  276  volts.  The  curves  after 
passing  the  critical  pressure  are  parallel. 

The  discharge  through  helium,  which  was  also  studied  by  Strutt, 
presents  many  interesting  features.  Ramsay  and  Collie  *  first  drew 
attention  to  the  ease  with  which  the  discharge  passed  through 


-2 
I 

I 

I 
o 
— 

I 


800 


400 


300 


\ 


10  20  30  40  50  60 

Pressure  in  Millimetres  of  Mercury 
Fig.  103.     Helium. 


helium.    Strutt's  experiments,  the  results  of  which  are  represented 
in  Fig.  103,  show  that  for  a  given   length  of  spark  the  critical 


Ramsay  and  Collie,  Proc.  Roy.  Soc.  lix.  p.  257,  1896. 


366 


SPARK   DISCHARGE. 


[186 


pressure  is  exceedingly  high,  being  about  5  times  that  of  air  for 
the  same  spark  length  and  more  than  twice  that  of  hydrogen.  The 
great  effect  of  small  impurities  on  the  minimum  spark  potential 
is  shown  by  the  different  curves  in  Fig.  103,  which  refer  to  samples 
purified  in  different  ways :  the  smallest  value  of  this  potential 
obtained  by  Strutt  was  261  volts. 

186.  We  have  seen  that  the  product  of  the  critical  pressure  and 
the  spark  length  is  constant  and  is  also  independent  of  the  nature 
of  the  electrodes,  it  is  thus  a  property  of  the  gas  :  the  following  table 
contains  the  values  of  this  product  q,  calculated  from  the  measure- 
ments of  Carr  and  Strutt,  and  also  the  mean  free  paths  (X)  of  the 
molecules  of  the  gases  at  atmospheric  pressure,  these  with  the 
exception  of  helium  are  taken  from  the  table  in  0.  E.  Meyer's 
Kinetische  Theorie  der  Gase,  p.  142,  that  of  helium  is  deduced  from 
Lord  Rayleigh's*  experiments  on  the  viscosity  of  helium :  though 
these  free  paths  are  taken  for  a  particular  pressure,  the  ratio  of 
the  free  paths  of  the  molecules  of  different  gases  is  independent 
of  the  pressure.  The  numbers  in  column  (3)  are  the  spark  length 
in  millimetres  multiplied  by  the  critical  pressure : 


Gas 

Minimum  spark 
potential 

2 

X  x  105  cm. 

105  x  \lq 

Air 

341  S. 

5-7 

•95 

•17 

Nitrogen     .  .. 

251  S.  * 

6-7 

•98 

•14 

Oxygen    . 

455  C. 

1-05 

Hydrogen    

(302—308  S.) 

14-4 

1-8 

•12 

Carbonic  acid 

(      278  C.     J 
419  C. 

5-1 

•68 

•13 

Sulphur  dioxide  

457  C. 

3-3 

•48 

•14 

Nitrous  oxide 

418  C 

5 

•68 

•14 

Sulphuretted  hydrogen 
Acetylene   

414  C. 
468  C. 

6 

•628 

•10 

Helium   

261  S. 

27 

2-6 

•10 

The  letters  S.  and  C.  indicate  that  the  measurements  were 
made  by  Strutt  or  Carr :  no  very  great  accuracy  can  be  claimed 
for  the  values  of  q,  as  the  determination  of  the  critical  pressure  is 
difficult;  a  small  error  in  the  determination  of  the  spark  potential 
near  this  pressure  would  lead  to  a  large  error  in  the  value  of  the 


Lord  Rayleigh,  Proc.  Roy.  Soc.  Ixix.  p.  198,  1896. 


187]  SPARK    DISCHARGE.  367 

critical  pressure.  Taking  this  into  account,  I  think  the  differences 
shown  in  the  preceding  table  for  q/\  from  the  constant  value 
1*3  are  not,  except  in  the  case  of  sulphuretted  hydrogen  and 
helium,  greater  than  might  be  explained  by  errors  of  experiment. 
In  the  two  exceptions  sulphuretted  hydrogen  and  helium  there 
are  special  circumstances  which  make  us  hesitate  to  accept  the 
results  as  final  without  further  experiment.  Sulphuretted  hydro- 
gen is  decomposed  by  the  spark,  hydrogen  being  liberated;  if  such 
a  decomposition  had  occurred  in  the  experiments  we  have  used 
for  the  determination  of  q  the  spark  would  have  passed  through  a 
mixture  of  hydrogen  and  sulphuretted  hydrogen,  the  hydrogen 
would  increase  the  critical  pressure  and  hence  the  value  of  q. 
Again  as  Strutt's  experiments  show,  the  numbers  for  helium  are 
very  greatly  affected  by  the  presence  of  small  amounts  of  impurity, 
so  that  it  would  hardly  be  safe  to  draw  conclusions  from  this  gas 
unless  the  free  path  determination  had  been  made  with  the  same 
specimen  of  gas  as  the  electrical  determinations. 

We  may,  I  think,  conclude  that  for  a  large  number  of  gases 
the  value  of  qj\  is  approximately  constant,  i.e.  that  with  a  given 
spark  length  the  critical  pressure  is  proportional  to  the  mean  free 
path  of  the  molecules  of  the  gas. 


Paschen  s  Law. 

187.  As  the  result  of  a  very  numerous  series  of  experiments  on 
the  relation  between  spark  potential  and  pressure,  Paschen*  came 
to  the  conclusion  that  the  spark  potential  depended  only  upon  the 
product  of  the  pressure  and  the  spark  length :  i.e.  upon  the  mass 
of  gas  between  unit  area  of  the  electrodes.  Thus,  if  the  spark 
length  d  and  pressure  p  of  the  gas  are  both  altered,  but  in  such  a 
way  that  their  product  does  not  change,  the  spark  potential  V 
will  remain  constant ;  or  in  other  words  V  is  a  function  of  pd. 

The  following  results  taken  from  Paschen's  paper  show  how 
nearly  the  law  is  obeyed  over  the  range  of  pressures  studied  by 
him ;  all  these  pressures  it  ought  to  be  noticed  are  considerably 
above  the  critical  pressures.  V  is  the  spark  potential  measured  in 
electrostatic  units,  p  the  pressure  measured  in  cm.  of  mercury, 

*  Paschen,  Wied.  Ann.  xxxvii.  p.  79,  1889. 


368  SPARK   DISCHARGE.  [187 

and  d  the  spark  length  in  cm.:  the  electrodes  in  these  experiments 
were  spheres  1  cm.  in  radius. 


Air :  pd  =  7'5 


P 

d 

V 

10 

0-75 

16-23 

15 

0-50 

16-54 

20 

0-38 

16-75 

25 

0-30 

17-00 

30 

0-25 

16-83 

40 

0-17 

16-86 

50 

0-15 

16-68 

75 

o-i 

16-33 

Mean 

16-65 

Hydrogen :  pd=7'5 


P 

d 

F 

10 

0-75 

9-50 

15 

0-50 

9-32 

20 

0-38 

9-47 

25 

0-30 

9-59 

30 

0-25 

9-58 

40 

0-187 

9-69 

50 

0-15 

9-90 

75 

o-io 

10-44 

Mean 

9-68 

Carbonic  acid :  pd=7'5 


P 

d 

F 

12-5 

0-6 

16-45 

15-0 

0-5 

16-48 

20-0 

0-38 

17-02 

25-0 

0-30 

17-92 

30-0 

0-25 

17-79 

40-0 

0-187 

18-33 

50-0 

0-15 

17-77 

75-0 

o-io 

17-21 

Mean 

17-37 

Air :  pd  =  20 


p 

d 

F 

28-6 

0-7 

34-30 

33-3 

0-6 

34-63 

40-0 

0-5 

35-12 

50-0 

0-4 

34-77 

66-66 

0-3 

35-39 

Mean 

34-64 

Hydrogen  :  pd  =  20 


p 

d 

F 

28-6 

0-7 

"  19-12 

33-33 

0-6 

19-25 

40-00 

0-5 

19-43 

50-00 

0-4 

19-43 

68-66 

0-3 

20-00 

Mean 

19-45 

Carbonic  acid  :  pd  =  20 


P 

d 

F 

33-33 

40-00 
50-00 
6666 

0-6 
0-8 
0-4 
0-3 

Mean 

33-03 

32-86 
33-46 
34-11 

33-6 

187] 


SPARK   DISCHARGE. 


369 


The  relation  between  the  spark  potential  and  the  product  pd 
is  shown  in  the  curves  for  air,   hydrogen,  and  carbonic  acid  in 


^ 

x 

•^ 

r 

s 

X 

^ 

'„- 

X 

' 

Nv 

x 

X 

,,- 

& 

)  I* 

^x 

> 

X^ 

- 

. 

\ 

^ 

x  '' 

J 

-' 

"J 

x 

, 

'A 

rO 

°^e 

^  ^ 

« 

Xf 

* 

ft 

-• 

" 

^ 

r 

"}     OQ 

t 

x 

= 

.-- 

>-^ 

,; 

? 

- 

,/ 

„ 

^ 

* 

' 

J 

- 

' 

s  ' 

0 

It 

1 

I 

\- 

2( 

D 
Fi 

J.  - 

LO^ 

L 

3 

D 

4 

9 

Fig.  104,  the  ordinates^are  the  spark  potentials  in  electrostatic 
measure,  the  abscissae  the  values  of  pd. 


O 

I 
I 

Q      AM 


2  mrr 


5  mr> 
/O. 


Product  of  Pressure  and  Distance  between  Electrodes 
Fig.  105.     Air. 

Paschen's  experiments  were  all  made  at  pressures  considerably 
greater  than  the  critical  pressure ;  it  has,  however,  quite  recently 
T.  G.  24 


370 


SPARK  DISCHARGE. 


[187 


been  shown  by  Carr  (I.e.)  that  Paschen's  law  holds  at  all  pressures. 
This  is  very  clearly  shown  by  the  curves  in  Figs.  105,  106,  which 


I 

\ 

+ 
X 

</- 
</- 

/  /T7/7 
2/TT/7 

+=» 

3  * 

\ 

• 
0 

d  = 
of  - 

5  mr 
/O  mr 

.2 

\ 

a 

o>     ^ 

n    /ceo 
1 

\ 

ft    *° 

"eS 

\ 

1  * 

V 

»***L 

DTT-4U 

w-a 

A^ 

•»-** 

K3     g> 

»•* 

-»*— 

•t« 

=±=f 

/  2 

Product  of  Pressure  and  Distance  between  Electrodes 


Fig.  106.     Carbon  Dioxide. 


represent  the  relation  between  the  spark  potential  V  (in  this  case 
measured  in  volts)  and  the  product  pd  (p  was  measured  in  milli- 
metres of  mercury  and  d  in  millimetres) ;  five  different  values  of  d 
were  used,  ranging  from  1  to  10  mm. ;  the  results  of  these  are 
represented  on  the  curve  by  symbols  attached  to  the  points  on  the 
curve  determined  by  the  various  experiments.  It  will  be  seen 
that  the  points  for  all  the  spark  lengths  all  lie  on  the  same  curve, 
and  in  this  case  the  range  of  pressures  extended  far  below  the 
critical  pressure.  The  results  of  Paschen's  law  are  very  important; 
we  see  that  to  find  the  spark  potential  corresponding  to  any  spark 
length  and  any  pressure  it  is  only  necessary  to  possess  the  results 
of  experiments  made  with  a  constant  spark  length  over  the  whole 
range  of  pressures.  We  see,  too,  that  it  follows  from  this  law  that 
the  critical  pressure  must  vary  inversely  as  the  spark  length,  a 
result  for  which  as  we  have  seen  there  is  direct  experimental 
evidence.  It  follows  too  from  this  law  that  if  we  know  the  values 
of  the  spark  potential  required  to  produce  a  spark  of  constant 
length  for  all  pressures  we  can  deduce  the  value  of  the  spark 
potential  for  a  spark  of  any  length  at  any  pressure. 


188] 


SPARK  DISCHARGE. 


371 


X188.  For  pressures  considerably  greater  than  the  critical 
pressure  the  relation  between  the  spark  potential  and  the  spark 
length  is  a  linear  one;  if  Fis  the  spark  potential  and  a;  the  spark 
length  at  atmospheric  pressure,  then 

F=  ax  +  b, 

where,  if  V  is  measured  in  electrostatic  units  and  x  in  centi- 
metres, the  experiments  by  Bailie,  Liebig,  Paschen,  Orgler  give 
the  following  values  for  the  constants  in  hydrogen,  air,  and 
carbonic  acid. 


Gas 

BAILLE 

LIEBIG 

PASCHEN 

ORGLER 

a 

6 

a 

& 

a 

& 

a 

6 

Air 

99-6 

5 

87'4 
55-8 
91-8 

92'5 
43-0 
91-1 

93-6 
46-3 
85-6 

Hydrogen   ... 
Carbonic  acid 

Wolf*,  who  measured  the  spark  potential  required  to  produce 
a  spark  1  mm.  long  at  pressures  varying  from  1  to  5  atmo- 
spheres, found  that  (as  we  should  expect  from  Paschen's  law)  the 
relation  at  these  high  pressures  between  spark  potential  and  pres- 
sure is  a  linear  one ;  if  V  is  the  spark  potential  in  electrostatic 
measure  and  x  the  pressure  in  atmospheres,  then  Wolf  found  that 
V  was  given  by  the  following  expressions : 

For  hydrogen         V=  6*509  x  +  6'2 
For  oxygen  F=9'6#       +  4'4 

For  air  F=10'7^     +  3'9 

For  nitrogen  F  =  I2'08x  +  5'0 

For  carbonic  acid  V=  10'22#  +  7*2. 

If  F  is  the  average  electric  force  between  the  electrodes 
in  these  experiments,  then  ^T=10F. 

The  order  of  the  spark  potential  for  different  gases  as  will  be 
seen  from  the  preceding  table  depends  upon  the  pressure ;  thus 
at  the  pressure  of  1  atmosphere  F  for  CO2  is  greater  than  F  for 
air,  while  at  high  pressures  it  is  less. 


*  Wolf,  Wied.  Ann.  xxxvii.  p.  306,  1889. 


24—2 


372  SPARK   DISCHARGE.  [189 

189.  Bouty*  has  made  a  series  of  experiments  on  the  electric 
field  required  to  make  a  gas  into  a  conductor,  using  a  method  which 
dispensed  with  the  use  of  metallic  electrodes.  In  this  method  the 
gas  at  a  low  pressure  is  contained  in  a  glass  vessel  with  parallel 
sides,  and  this  vessel  is  placed  in  the  space  between  two  parallel 
plates  parallel  to  the  walls  of  the  vessel,  the  difference  of  potential 
between  these  plates  is  increased  until  the  gas  in  the  glass  vessel 
becomes  luminous,  indicating  that  a  discharge  is  passing  through 
it;  the  strength  of  the  electric  field,  i.e.  the  electric  force  (not  the 
potential  difference),  when  this  occurs  is  called  by  Bouty  the  cohe- 
sion dielectrique  of  the  gas.  A  very  considerable  number  of  gases 
were  examined  by  this  method.  Bouty  found  that  the  cohesion 
dielectrique  F  for  gases  up  to  6  cm.  pressure  could  be  represented 
by  the  formula 

F=a  +  bp, 

where  a  and  b  are  constants  and  p  is  the  pressure.  When  F  is 
measured  in  absolute  electrostatic  units  and  p  in  atmospheres, 
Bouty  found  that 

For  hydrogen        F  =  1-4      +  63'33^ 
For  air  F=  T593  +  119'09j9 

For  carbonic  acid  ,F=  T703  +  144*4  p; 

he  compares  these  expressions  with  those  given  by  Wolf  and 
points  out  that  while  the  coefficients  of  p  are  not  so  very  different 
the  constant  terms  are  of  quite  a  different  order;  he  ascribes  this 
difference  to  the  electrodes  in  Wolfs  experiments  being  metal, 
while  in  his  experiments  they  were  glass;  it  seems  to  me  that  the 
following  explanation  is  more  probable.  If  V  is  the  potential 
difference  required  to  produce  a  spark  of  length  I  through  gas  at 
a  pressure  p  considerably  greater  than  the  critical  pressure,  then 
we  have  approximately,  if  A  and  B  are  constants, 


since  we  know  by  Paschen's  law  that  F  is  a  function  of  Ip  ;  hence 
F,  the  average  electric  intensity  when  the  spark  passes,  is  given 
by  the  equation 


hence  the  constant  term  varies  inversely  as  the  length  of  the  spark 
*  Bouty,  C.  R.  131,  p.  469,  1900. 


189] 


SPARK   DISCHARGE. 


373 


while  the  coefficient  of  p  is  independent  of  the  spark  length.  In 
Wolf's  experiments  the  spark  length  was  only  1  mm.,  while  the 
distance  between  the  plates  in  Bouty's  experiments  was  much 
greater  so  that  the  difference  in  the  spark  length  would  explain  the 
difference  in  the  constant  term,  and  it  is  not  necessary  to  ascribe 
it  to  the  nature  of  the  electrodes.  Bouty*  has  determined  the 
constants  a,  b,  in  the  expression  F=a-)-bp  for  the  cohesion 
dielectrique  for  a  number  of  vapours,  the  results  are  given  in 
the  following  table.  Bouty's  measurements  were  made  at  pres- 
sures ranging  from  '0055  cm.  to  2  cm.  of  mercury.  The  constants 
apply  when  the  pressure  is  measured  in  cm.  of  mercury  and  F  in 
volts  per  cm. 


Vapour  of 

a 

b 

Water 

333 

500 

Methyl-alcohol  ... 
Ethyl-alcohol  
Ether  

375 

364 
360 

616 

800 
1000 

Methyl  formate  ... 
Ethyl  propionate 
Acetone 

364 
312 
355 

1020 
1083 
1100 

Ethyl  formate  
Methyl  acetate  .  .  . 
Carbon  bisulphide 
Toluol 

360 
369 
330 

380 

1110 
1250 
1510 
1610 

Benzol  . 

377 

1670 

It  will  be  seen  that  the  values  of  a  vary  very  little  in  com- 
parison with  those  of  b.  The  values  of  b  are  in  nearly  every 
case  in  the  same  order  as  those  of  1/X,  where  X  is  the  mean  free 
path  of  the  molecules  of  the  gas,  and  are  in  many  cases  roughly 
proportional  to  this  quantity.  If  the  law  which  is  suggested  by 
these  results  actually  holds  and  b  is  inversely  proportional  to  1/X 
the  spark  potential  V  required  for  a  constant  spark  length  must 
at  pressures  greater  than  the  critical  pressure  be  expressed  by  an 
equation  of  the  form 


where  X  is  the  mean  free  path  of  the  molecules  and  a  and  b  are 
constants  which  are  the  same  for  all  gases. 

*  Bouty,  C.  E.  131,  p.  503,  1900. 


374  SPARK   DISCHARGE.  [190 

190.  v.  Rontgen*  arrived  at  the  conclusion  that  the  spark 
potential  for  a  constant  spark  length  was  inversely  proportional  to 
the  mean  free  path  of  the  molecules  of  the  gas  through  which  the 
spark  passed ;  we  have  seen,  however,  that  the  ratio  of  the  spark 
potential  for  different  gases  varies  with  the  pressure  and  the  spark 
length,  so  that  this  statement  does  riot  give  complete  expression 
to  the  laws  of  the  spark -discharge.  If  we  look  at  the  question 
from  the  point  of  view  of  Paschen's  law  we  see  that  from  that  law 

F=/Y? 


where  x  is  the  spark  length  and  X  the  mean  free  path  of  the  mole- 
cules of  the  gas;  if  the  spark  potential  for  different  gases  depended 
only  upon  the  mean  free  path  of  the  molecules  of  the  gases  the 
function  /  would  be  the  same  whatever  were  the  nature  of  the 
gas ;  but,  if  this  were  the  case  the  minimum  potential  required 
to  produce  a  spark  would  be  the  same  for  all  gases,  a  result  which 
is  inconsistent  with  the  determinations  made  of  this  quantity.  I 
have  tried  an  equation  of  the  form 


where  F  is  the  same  function  for  all  gases  and  A  a  constant  which 
may  vary  from  one  gas  to  another.  Practically  the  only  gases  for 
which  we  possess  sufficient  materials  to  test  this  law  adequately 
are  air,  hydrogen  and  carbonic  acid.  I  have  found  that  the  obser- 
vations in  air  and  hydrogen  are  in  fair  agreement  with  this  law, 
while  those  in  carbonic  acid  are  not :  it  is  desirable,  however,  that 
the  law  should  be  tested  over  a  far  wider  range  of  gases,  as  there 
are  special  circumstances  connected  with  carbonic  acid  which  make 
one  hesitate  to  accept  conclusions  drawn  from  this  gas  alone;  in  the 
first  place  the  experiments  made  by  different  observers  differ 
more  widely  for  this  gas  than  for  any  of  the  others  tested,  it  is 
one  in  which  the  'lag'  of  the  spark  is  exceedingly  pronounced,  and 
in  other  cases  of  discharge,  such  for  example  as  that  produced  by 
ultra-violet  light,  it  exhibits  peculiarities  not  shown  by  air  or 
hydrogen.  Careful  observations  on  the  spark  discharge  in  a  gas 
which  has  a  mean  free  path  differing  considerably  from  either 
hydrogen  or  air  are  much  wanted. 

*  Rontgen,  Gottingen  Nach.  1878,  p.  390. 


191] 


SPARK   DISCHARGE. 


375 


191.  Natterer*  tested  for  a  large  number  of  gases  the  length 
of  spark  produced  at  constant  pressure  by  a  small  induction  coil ;  the 
measurements  made  by  this  method  are  of  necessity  exceedingly 
rough  but  they  are  for  many  gases  the  only  measurements  we 
possess  relating  to  the  passage  of  the  spark.  Part  of  Natterer's 
results  are  given  in  the  following  table,  the  temperature  when  not 
stated  is  to  be  taken  as  about  20°  C.,  the  spark  lengths  are  in 
millimetres. 


Gas 

Spark  length 

Gas 

Spark  length 

H2.                 

15—20 

HCN  (80°  C.)   . 

2—3 

No   

10—15 

CO  

10—14 

NO 

9     14 

C«H, 

8—13 

O2 

8—10 

C2He             

10—13 

HC1 

5—7 

CH3OH  (100°  C.)  

9—12 

C12  

2—4 

C02    

8—11 

HBr  ... 

2—3-5 

CH3.CHO(100°C.)... 

6—8 

HI 

1-5  —  2 

CoH.OH  (110°  C)    . 

7     9 

Br2  (100°  C  ) 

2—3 

CH3C1   

8—11 

I9  (230°  C  )    . 

2-5—3 

C2N2  

1-5—2 

H20  (130°  C.)   ...     . 

4—7 

(CHA,CO  (100°  C.)  .. 

6—9 

H2S   ...    . 

3—5 

C2H6CHO  (100°C.)... 

4—7 

N00 

3—5 

C2H5C1 

4    7 

S02    

1-5—2 

(C2H6)20  (100°  C.)   ... 

5—8 

HgCl2  (271°  C  ) 

2—2-5 

CS2(100°C.)  

2—3 

5—8 

C6H6  (110°  C.)  

7—9 

p|33  :::;:;:  

4—7 

C4H4S  (110°  C.)    

4—5 

SoCL  (135°C.)  .. 

1-75—2 

C2H302C2H5(110°C.) 

3—7 

PC13  (137-5°  C.)    
AsCl3(181-5°C.)  
PBr3(271°C.)  

1-5—2 
1-25—1-5 
l-75_2 

C2H5Br  (100°  C.)  
CHC13(100°C.)    
C3H7Br  (100°  C.)  

3—3-5 

1-75—2 
2-25—2-75 

SiF4(101°C.)    

5—7 

(CH'3)2CHBr  (100°  C.) 

2—2-5 

PC130(153°C.) 

2-25—2-5 

CH3I  (100°  C.)  

2—2-25 

SiCl4(170°C.) 

1-75—2 

OGL(110°C.)  

1-5—1-75 

SnCL  (260°  C.) 

1-5—1-75 

C2H5I  (100°  C.)    

1-75—2 

CH/ 

7—10    ' 

CHBro  (180°C.)  ., 

2—2-5 

C9H9  . 

3—4 

Hg(£uSA,(1950C.)... 

6—7 

It  will  be  noticed  that  the  spark  lengths  are  short  in  vapours 
of  complicated  chemical  constitution  in  which  the  mean  free  paths 
are  small ;  the  halogen  elements  chlorine,  bromine  and  iodine  seem 
to  exert  a  great  influence  in  shortening  the  spark,  these  elements 
and  their  compounds  have  short  free  paths. 

Natterer  found  that  the  spark  length  was  exceptionally  long 


*  Natterer,  Wied,  Ann.  xxxviii.  p.  63,  1889. 


376  SPARK   DISCHARGE.  [192 

in  the  monatomic  vapours  of  mercury  and  cadmium,  we  have  seen 
that  it  is  also  long  in  the  monatomic  gas  helium. 

Theory  of  the  Spark  Discharge. 

192.  At  this  stage  it  may  be  useful  to  give  an  account  of 
a  theory  which  explains  many  of  the  peculiarities  of  the  spark 
discharge.  On  this  theory,  which  was  given  by  the  writer  in 
a  paper  read  before  the  Cambridge  Philosophical  Society,  Feb. 
1900,  and  published  in  the  Philosophical  Magazine,  [5],  50,  p.  278, 
1900,  the  ionisation  which  is  necessary  to  put  the  gas  into  the 
conducting  state  required  for  the  passage  of  the  spark  is  effected 
by  means  of  ions  which  under  the  influence  of  the  electric  field 
producing  the  spark  acquire  so  great  a  velocity  that  when  they 
come  into  collision  with  the  molecules  of  the  gas  through  which 
they  are  moving  they  ionise  the  molecules.  We  have  already  had 
instances  of  the  ionisation  of  a  gas  by  rapidly  moving  ions  in  the 
cases  of  cathode  and  Lenard  rays,  and  we  have  seen  that  the  view 
(which  was  suggested  by  the  consideration  of  the  spark  discharge) 
that  ions  in  a  strong  electric  field  can  acquire  sufficient  energy  to 
enable  them  to  act  as  ionising  agents  was  of  service  in  explaining 
some  of  the  phenomena  connected  with  the  discharge  of  electri- 
city produced  by  the  action  of  ultra-violet  light.  Townsend  (see 
p.  341)  has  shown  that  in  the  case  of  a  gas  ionised  by  means  of 
Rontgen  rays  the  negative  corpuscles'  present  in  the  gas  can  in 
a  strong  electric  field  produce  fresh  ions  by  their  collision  with 
the  molecules  of  the  gas ;  we  have  tnus  from  several  sources 
direct  evidence  that  rapidly  moving  negative  ions  can  by  means 
of  collision  give  rise  to  fresh  ions. 

Let  us  now  consider  the  case  of  a  gas  between  two  parallel 
metal  plates,  between  which  there  is  an  electric  field,  then  if  there 
were  a  few  negative  ions  present  these  would  be  set  in  motion  by 
the  field,  and  if  the  strength  of  the  field  exceeded  a  certain  value 
would  acquire  sufficient  energy  to  ionise  the  molecules  of  the  gas 
with  which  they  came  into  collision,  fresh  ions  would  be  produced 
and  a  current  of  electricity  would  flow  through  the  gas.  If,  how- 
ever, the  conditions  are  such  that  only  the  negative  ions  in  the 
field  produce  fresh  ions,  this  current  will  only  be  transitory,  in  a 
short  time  all  the  negative  ions  will  be  driven  up  to  the  cathode 
and  the  current  will  stop.  If,  however,  the  positive  ions  in  their 


193]  SPARK  DISCHARGE.  377 

journey  to  the  cathode  can  produce  fresh  ions,  then  negative  ions 
are  continually  being  produced,  these  under  the  action  of  the  field 
will  produce  new  ions  and  so  the  number  of  the  ions  and  the 
conductivity  of  the  gas  will  increase  in  geometrical  progression ; 
this  increase  will  not,  however,  go  on  indefinitely,  for  with  the 
increased  conductivity  of  the  gas  the  strength  of  the  electric  field 
between  the  plates  will  diminish  until  it  falls  to  such  a  point  that 
the  number  of  ions  produced  in  unit  time  by  the  field  is  equal  to 
the  number  lost  in  the  same  time  through  the  combination  of  the 
ions  and  through  the  motion  of  the  ions  up  to  the  electrodes.  To 
maintain  the  current  it  is  not  necessary  for  the  positive  ions  to 
produce  fresh  ions  at  all  parts  of  the  field  between  the  electrodes, 
it  is  sufficient  for  them  to  do  so  close  to  the  cathode.  The  posi- 
tive ions  will  strike  against  the  cathode;  we  shall  suppose  that 
under  this  bombardment  by  the  positive  ions  the  cathode  emits 
negative  corpuscles — in  fact  cathode  rays — so  that  the  continuous 
supply  of  negative  corpuscles  comes  on  this  view  from  the  metal 
of  the  cathode  stimulated  by  the  positive  ions  striking  against  it. 
The  action  of  the  positive  ions  as  ionising  agents  is  thus  confined 
to  the  effect  produced  by  their  impacts  on  the  cathode,  it  is  not 
necessary  to  suppose  that  they,  like  the  negative  corpuscles,  ionise 
the  molecules  of  a  gas  by  striking  against  them.  The  expression 
for  the  potential  difference  is  however  the  same  whether  we  suppose 
that  the  positive  ions  cause  the  cathode  to  emit  corpuscles  by  their 
impact  with  it,  or  whether  we  suppose  that  they  ionise  the  gas 
close  to  the  cathode,  the  positive  ions  in  other  parts  of  the  field 
not  possessing  sufficient  energy  to  ionise  the  gas. 

193.  Before  attempting  to  obtain  by  these  principles  the  con- 
nection between  spark  potential,  spark  length  and  pressure  it  will 
be  helpful  to  consider  some  facts  as  to  the  distribution  of  electric 
force  along  the  spark,  obtained  by  the  study  of  the  discharge  at 
low  pressures  when  the  structure  of  the  discharge  is  much  more 
obvious  than  it  is  at  atmospheric  pressure.  This  structure  as  w$ 
shall  see  later  shows  many  variations,  but  an  example  which  may 
be  taken  as  typical  is  that  shown  in  Fig.  107.  The  distribution  of 
electric  intensity  along  the  line  of  discharge  is  shown  in  Fig.  108. 
Next  to  the  cathode  there  is  a  dark  space  called  the  Crookes  dark 
space,  the  thickness  of  which  does  not  depend  upon  the  distance 
between  the  electrodes,  then  comes  a  luminous  piece  called  the 


378 


SPAKK   DISCHARGE. 


[193 


negative  glow,  then  comes  a  dark  space  called  the  Faraday  dark 
space,  and  then  a  stretch  of  luminosity  reaching  to  the   anode, 


Fig.  107. 

called  the  positive  column.     From  the  curve  giving  the  electric 
intensity    we    see    that    this    is    approximately    uniform    along 


01234 

Positive  column 


12      13!    14 

Negative  glow 


Fig.  108. 


the  positive  column;  but  that  in  the  Crookes  dark  space  the 
electric  intensity  is  very  much  greater.     The  potential  difference 


193]  SPARK   DISCHARGE.  379 

between  the  cathode  and  the  negative  glow,  called  the  cathode 
potential  fall,  is  as  we  shall  see  later  independent  of  the  pressure 
of  the  gas  or  the  distance  between  anode  and  cathode,  as  long  as 
this  is  greater  than  the  thickness  of  the  dark  space.  Recent 
measurements  made  by  Strutt  have  proved  that  the  cathode  fall 
of  potential  is  equal  to  the  minimum  spark  potential.  We  see, 
too,  that  it  is  only  in  the  Crookes  dark  space  that  the  electric 
intensity  is  greater  than  in  the  uniform  positive  column,  it  is 
therefore  only  in  this  space  that  the  positive  ions  would  be  likely 
to  produce  fresh  ions  by  collisions  with  molecules  of  the  gas.  To 
sum  up  we  have  a  uniform  electric  intensity  along  the  positive 
column  and  a  variable  but  very  much  greater  intensity  inside  the 
Crookes  dark  space.  The  thickness  of  the  dark  space  does  not 
depend  upon  the  distance  between  the  electrodes,  so  that  the 
further  these  are  apart  the  longer  the  region  of  uniform  electric 
intensity  along  the  positive  column. 

We  shall  now  proceed  to  find  the  connection  between  the 
spark  potential  and  the  spark  length.  We  found  (p.  341)  that  if  n 
is  the  number  of  corpuscles  per  unit  volume  at  a  distance  x  from 
the  cathode,  u  the  velocity  of  these  corpuscles,  X  their  mean  free 
path,  e  the  charge  on  a  corpuscle,  then  when  the  system  is  in  a 
steady  state 


where  f(Xe\)  is  the  ratio  between  the  number  of  collisions  which 
produce  fresh  ions  and  the  whole  number  of  collisions,  and  7  the 
ratio  of  the  number  of  collisions  in  which  the  corpuscles  remain 
attached  to  the  molecule  to  the  whole  number  of  collisions.  If 
the  electric  field  is  very  strong  the  corpuscles  acquire  so  much 
energy  that  every  collision  produces  ions,  in  this  ca,SGf(Xe\)  =  l, 
if  Xe\  falls  below  a  certain  value  iheuf(Xe\)  =  0,  we  shall  sup- 
pose that  in  the  Crookes  dark  space  the  electric  field  is  so  strong 
that/(ZeX)  =  1,  and  that  in  the  rest  of  the  field  where  the  electric 
intensity  is  much  less  f(Xe\}  =  ftXe\  —  w,  where  ft  and  w  are 
constants. 

From  equation  (1)  we  have 
where  nQu0  is  the  value  of  nu  when  x  —  0,  i.e.  at  the  cathode;  if  we 


380  SPARK   DISCHARGE.  [193 

put  x  =  d  in  this  expression  we  shall  get  the  value  of  nu  at  the 
anode,  this,  if  no  positive  ions  come  from  the  anode  itself,  is  equal 
to  i/e,  where  i  is  the  current  per  unit  area  through  the  gas.  Let  us 
first  take  the  case  where  d  is  greater  than  c,  the  thickness  of  the 
Crookes  layer:  then  from  x=Q  to  x  =  c,  f(Xe\)  =  l)  and  from 
x  =  c  to  d,  f(Xe\)  =  13 Xe\  -  w,  hence  in  this  case, 

/^/v^\       \dx     c>Q*nr      v\      ^d     w(d-c) 

(f(Xe\)  —  7)  —  =  -  4-  pe  (  V  —  VQ)  —  — , 

o     J  ^  X       X  X  X 

where  F0  is  the  fall  of  potential  in  crossing  the  Crookes  dark 
space,  i.e.  the  cathode  fall  of  potential.  Hence  we  have  from  (2) 
putting  nu  =  i/e 


Now  n0u0  is  the  number  of  corpuscles  emitted  in  unit  time  by 
unit  area  of  the  cathode.  We  suppose  that  this  emission  is  due 
to  the  bombardment  of  the  cathode  by  the  positive  ions,  and  that 
the  number  of  corpuscles  emitted  per  second  is  proportional  to  the 
energy  given  to  the  cathode  by  the  positive  ions.  The  question 
now  arises  as  to  the  energy  possessed  by  the  ions  when  they  strike 
the  cathode  ;  before  they  reach  the  Crookes  space  they  are  moving 
in  a  weak  part  of  the  field,  and  their  energy  is  proportional  to  Xe\ 
where  X  is  the  electric  intensity  ;  when  however  they  get  into  the 
dark  space  the  field  rapidly  becomes  more  intense,  and  the  energy 
of  the  positive  ions  rapidly  increases,  we  shall  therefore  get  a  close 
approximation  to  the  truth  if  we  suppose  that  the  energy  of  the 
positive  ions  is  given  to  them  in  the  dark  space,  and  that  the  energy 
of  each  ion  is  equal  to  V0e,  V0  being  the  cathode  fall  of  potential. 
The  number  of  positive  ions  which  strike  unit  area  of  the  cathode 
in  unit  time  is  (i—  w0w0e)/e,  and  the  energy  given  up  by  these  to 
the  cathode  is  therefore  (i  —  w0^0e)F0.  We  suppose  that  n0u0 
the  number  of  corpuscles  emitted  in  unit  time  is  proportional  to 
the  energy  of  bombardment,  so  that 

n0u0  =  k(i  —  n0u0  e)  F0  , 
where  A;  is  a  constant. 

Substituting  this  value  of  n0uQ  in  equation  (3)  we  get 


_ 
- 


193]  SPARK   DISCHARGE.  381 

hence  we  have 


or 

F=  F  -f- 


X       $e         pe     X* 

This  gives  us  the  relation  between  F  the  spark  potential,  d  the 
spark  length  and  X,  which  is  inversely  proportional  to  the  pressure. 
We  see  that  the  relation  is  a  linear  one,  and  since  c  is  proportional 
to  X  we  see  also  that  this  equation  satisfies  Paschen's  law  that 
F  is  a  function  of  d/\, 

We  shall  return  to  the  discussion  of  this  equation  after  we 
have  considered  the  case  when  d  the  spark  length  is^ftss  than  c, 
i.e.  when  the  anode  comes  into  the  Crookes  dark  space.  In  this 
casef(Xe\)  is  equal  to  unity  throughout  the  field,  and  the  energy 
with  which  the  positive  ions  strike  the  cathode  is  now  eFand  not 
eV0,  where  F  is  the  potential  difference  between  the  plates.  Hence 
we  have 

,cfo?  d 


and  nQUoe  =  k(i  —  n0u0e)  Ve (5). 

Hence  instead  of  equation  (3)  we  have 


from  which  we  get 

1  +  kVe 


or  =~ 

ke 


€  A—  1 

from  this  equation  we  see  that  V  the  spark  potential  increases 
very  rapidly  as  d/\  diminishes  ;  we  see  too  that  Paschen's  law  is 
again  obeyed  since  F  is  a  function  of  d/\. 

If  we  combine  equations  (4)  and  (6),  and  represent  the  result 
graphically  by  a  curve  whose  ordinates  are  proportional  to  F  and 
abscissae  to  d/\,  we  get  a  curve  similar  to  that  shown  in  Fig.  109. 
A  reference  to  the  figures  given  on  pages  360  —  5  will  show  that 
except  just  in  the  neighbourhood  of  the  minimum  spark  potential 
the  theoretical  curve  agrees  well  with  those  determined  by  experi- 


382 


SPARK   DISCHARGE. 


[193 


ment ;  we  could  have  anticipated  the  want  of  smoothness  of  the 
theoretical  curve  in  this  region,  for  here  to  simplify  the  calculation 


Fig.  109. 

we  assumed  values  for  f(Xe\)  which  were  discontinuous  at  this 
point. 

It  is  of  interest  to  see  what  light  the  theory  throws  on  the 
questions  raised  by  the  experiments.  We  saw  that  the  measure- 
ments made  on  the  spark  potential  suggest  (we  can  hardly  use 
a  stronger  term)  that  the  spark  potential  could  be  expressed  by 

an  equation   of  the   form  V=k +/(-},  where  d  is  the  spark 

\X/ 

length,  and  X  the  mean  free  path,  and  /  a  function  which  is  the 
same  for  all  gases.  Now  for  sparks  whose  length  is  greater  than 

the  critical  spark  length  the  theory  gives  V=  constant  +  ^--5 — ™ ; 

/j6      A 

if  this  is  of  the  form  under  discussion  (>y+w)//3e  must  be  independent 
of  the  nature  of  the  gas :  7  measures  the  chance  of  a  corpuscle 
sticking  to  a  molecule  against  which  it  strikes,  and  ft  and  w  the 
chance  of  a  molecule  being  ionised  when  struck  by  a  corpuscle 
moving  with  a  given  velocity.  We  have  not  any  independent 
measurements  of  these  quantities ;  we  should  anticipate  that  they 
would  depend  to  some,  although  probably  not  to  any  large  extent, 


194]  SPARK   DISCHARGE.  383 

on  the  nature  of  the  molecule.  We  saw  too  (p.  366)  that  there  is 
considerable  evidence  that  for  a  given  pressure  the  critical  spark 
length  in  different  gases  is  proportional  to  the  mean  free  paths  of 
the  molecules  :  thus  if  c  is  the  critical  spark  length  when  the  free 
path  is  X,  c/\  is  the  same  for  all  gases. 

Let  us  now  consider  the  minimum  potential  F0  required 
to  produce  a  spark  ;  by  equations  (4)  and  (6)  this  is  given  by  the 
equation 


Thus  neglecting  variations  in  7  we  see  that  the  values  of  F0 
in  different  gases  are  proportional  to  I/ke.  From  equation  (5) 
it  follows  that  l/ke  is  the  potential  difference  through  which 
a  positive  ion  must  fall  in  order  to  acquire  such  an  amount  of 
energy  that  when  it  strikes  against  the  cathode  it  produces  the 
emission  of  one  corpuscle,  either  from  the  cathode  itself  or  from 
a  layer  of  gas  next  the  cathode. 

194.  This  view  we  have  taken  of  the  spark  discharge  accounts 
for  the  '  lag,'  i.e.  the  interval  between  the  application  of  the  electric 
field  and  the  passage  of  the  spark  which,  as  we  have  seen,  is  very 
noticeable  under  certain  circumstances.  For  before  the  spark 
reaches  a  steady  state  there  is  a  preliminary  stage  during  which 
the  number  of  ions  is  continually  increasing.  On  the  first  appli- 
cation of  the  field  the  number  of  ions  and  the  current  through  the 
gas  is  small,  but  in  consequence  of  the  collisions  of  these  ions  with 
the  molecules  of  the  gas,  the  number  of  ions  and  the  current 
rapidly  increase  until  finally  a  steady  state  is  reached  :  this  interval 
is  what  we  have  called  the  '  lag,5  and  we  see  that  its  duration  will 
be  diminished  by  any  agent,  such  as  ultra-violet  light  shining  on 
the  negative  electrode,  which  increases  the  number  of  negative 
ions  initially  in  the  gas. 

The  view  that  the  emission  of  negative  corpuscles  from  the 
cathode  is  due  to  the  impact  against  it  of  the  positive  ions  is 
strongly  supported  by  some  experiments  made  by  Schuster*  and 
Welmeltf  on  the  effect  of  placing  solid  obstacles  in  the  Crookes 
dark  space  :  these  obstacles  cast  a  shadow  on  the  cathode,  and 

*  Schuster,  Proc.  Roy.  Soc.  xlvii.  p.  557,  1890. 
t  Wehnelt,  Wied.  Ann.  Ixvii.  p.  421,  1899. 


384  SPARK   DISCHARGE.  [195 

from  the  region  of  this  shadow  there  is  no  emission  of  cathode  rays. 
This  effect  is  illustrated  in  Fig.  110,  taken  from  Wehnelt's  paper ; 
in  this  figure  D  is  the  obstacle  and  K  the  cathode. 


1 


K  D 

Fig.  110. 

Potential  difference  required  to  produce  very  short  sparks. 

195.  Earhart*  has  made  a  series  of  experiments  on  the  differ- 
ence of  potential  required  to  produce  sparks  whose  length  is 
comparable  with  the  wave-length  of  sodium  light ;  the  electrodes 
used  were  steel  spheres,  and  the  connection  between  the  spark 
potential  and  the  distance  between  the  spheres  is  shown  in  Fig.  Ill, 
in  which  the  abscissae  are  the  spark  potential  and  the  ordinates 
the  shortest  distance  between  the  spheres.  In  consequence  of  the 
curvature  of  the*  electrodes,  the  least  distance  between  the  spheres 
is  not  necessarily  equal  to  the  spark  length ;  thus  when  the 
distance  is  less  than  the  critical  spark  length  the  spark  will  pass, 
not  across  the  shortest  distance,  but  across  a  place  where  the 
distance  is  equal  to  the  critical  spark  length.  Thus  Earhart's 
curves  do  not  show  the  increase  in  potential  difference  with 
diminishing  distance  between  the  electrodes  as  they  would  have 
done  if  they  had  been  plane :  the  most  interesting  feature  of  the 
curves  is  the  very  rapid  diminution  in  the  spark  potential  when 
the  distance  between  the  electrodes  falls  to  less  than  about 
3  x  10~4  cm. ;  when  the  distance  is  less  than  this  the  spark 
potential  falls  off  rapidly  with  the  distance,  and  seems  from 
Earhart's  results  to  become  directly  proportional  to  the  distance. 
The  smallest  potential  difference  actually  measured  was  32  volts 
when  the  distance  Between  the  electrodes  was  3  x  10~5  cm. :  this 
is  only  about  one-tenth  of  the  minimum  spark  potential.  Earhart 
made  some  observations  on  the  effect  of  pressure ;  diminution 

*  Earhart,  Phil.  Mag.  vi.  1,  p.  147,  1901. 


195] 


SPARK   DISCHARGE. 


385 


of  the  pressure  from  three  atmospheres  to  one  atmosphere  did  not 
seem  to  affect  the  discharge  potential  when  the  electrodes  were 


00  200  300  40O  500  600  700  800  900  1000  1100 


Potential  in  Volts 
Fig.  111. 

very  close  together;  when  the  pressure  was  diminished  below 
one  atmosphere  however  the  discharge  potential  also  diminished. 
An  inspection  of  the  curves  suggests  that  the  character  of  the 
discharge  changes  when  the  electrodes  are  brought  within  a  certain 
distance  of  each  other,  or  what  is  equally  consistent  with  the 
curves,  when  the  average  electric  intensity,  F,  between  the  plates 
reaches  a  certain  value  (about  a  million  volts  per  cm.) :  when  F 
has  once  reached  this  value  Earhart's  experiments  suggest  that 
the  discharge  is  determined  by  the  condition  that  F,  i.e.  V/d, 
if  V  is  the  potential  difference  and  d  the  distance  between  the 
electrodes,  should  have  this  value.  These  experiments  raise  many 

25 


T.   G. 


386  SPARK   DISCHARGE.  [195 

important  points,  and  it  is  to  be  hoped  that  they  will  be  carried 
much  further. 

The  following  considerations  seem  to  afford  a  possible  explana- 
tion of  the  behaviour  of  the  discharge  when  the  electrodes  are 
very  close  together.  We  have  had  occasion  before  to  make  use 
of  the  hypothesis  that  in  a  metal,  even  at  ordinary  temperature, 
free  corpuscles  are  moving  about  in  every  direction;  if  these 
corpuscles  could  escape  from  the  metal  under  ordinary  conditions 
the  metal  would  be  unable  to  retain  a  charge  of  negative  electricity. 
Now  one  of  the  reasons  the  corpuscles  do  not  escape  is  that  as 
soon  as  they  leave  the  metal  there  is  an  electrostatic  attraction 
between  the  corpuscle  and  the  metal  equal  to  e2/4r2,  where  e  is  the 
charge  on  the  corpuscle  and  r  the  distance  of  the  corpuscle  from 
the  surface  of  the  metal ;  this  attraction,  unless  the  kinetic  energy 
with  which  the  corpuscle  leaves  the  metal  exceeds  a  certain  very 
high  limit,  will  drag  the  corpuscle  back  into  the  metal.  Let  us 
now  suppose  that  an  external  electric  force  F  acts  on  the  corpuscle, 
tending  to  make  it  move  away  from  the  metal ;  then  if  Fe  is 
comparable  with  e2/4r2,  the  external  field  will  give  appreciable 
assistance  to  the  corpuscle  in  escaping  from  the  metal,  and  will 
enable  corpuscles  to  leave  the  metal,  whose  kinetic  energy  is  too 
small  to  enable  them  to  escape  in  the  absence  of  an  external  field. 
If  Fe  is  comparable  with  e2/4r2,  F  must  be  comparable  with  e/4r2. 
Now  in  electrostatic  measure  e  =  3*4  x  10~10,  let  us  put  r  =  10~7, 
then  e/4r2  =  8'5  x  103.  Now  in  Earhart's  experiments  F  was  about 
106  volts  per  cm.,  or  in  electrostatic  measure  3*3  x  103;  this  is 
more  than  one-third  of  the  value  of  e/4r2,  so  that  if,  as  is  quite 
possible,  r  is  somewhat  greater  than  10~7,  the  pull  exerted  by  the 
external  field  would  be  able  to  drag  the  corpuscles  away  from  the 
metal :  as  soon  however  as  corpuscles  can  leave  the  electrode,  that 
electrode  will  act  like  a  cathode,  and  a  discharge  of  negative 
electricity  will  pass  from  this  to  the  opposite  electrode.  If  this 
explanation  is  correct  the  discharge  across  these  very-  small 
distances  is  entirely  carried  by  the  corpuscles  and  no  part  of  it 
by  positive  ions ;  in  the  discharge  we  have  previously  considered, 
corpuscles  and  positive  ions  both  take  a  share  in  carrying  the 
discharge. 


196] 


SPARK   DISCHARGE. 


387 


Discharge  when  the  electric  field  is  not  uniform. 

196.  Bailie*  and  Paschenf  have  made  some  very  interesting 
experiments  on  the  potential  difference  required  to  spark  between 
spheres  small  enough  to  make  the  variations  in  the  strength  of 
the  electric  field  considerable.  Bailie's  results  are  given  in  table  A» 
Paschen's  in  table  B  : 

A.    POTENTIAL  DIFFERENCES. 
Pressure  760  mm.,  Temp.  15°— 20°  C. 


Spark 
Length 
in  cms. 

Planes 

Spheres 
6cm. 
diam. 

Spheres 
3cm. 
diam. 

Spheres 
1  cm. 
diam. 

Spheres 
•6cm. 
diam. 

Spheres 
•35  cm. 
diam. 

Spheres 
•1  cm. 
diam. 

•05 

8-94 

8-96 

9-18 

9-18 

9-26 

9-30 

9-63 

•10 

14-70 

14-78 

14-99 

15-25 

15-53 

16-04 

16-10 

•15 

20-20 

20-31 

20-47 

21-28 

21-24 

21-87 

19-58 

•20 

25-42 

25-59 

25-95 

26-78 

26-82 

27-13 

21-91 

•25 

30-38 

30-99 

31-33 

32-10 

32-33 

31-96 

23-11 

•30 

35-35 

36-12 

36-59 

37-32 

37-38 

36-29 

24-12 

•35 

40-45 

41-45 

41-47 

42-48 

42-16 

39-39 

25-34 

•40 

45-28 

46-34 

46-77 

47-62 

46-34 

41-77 

26-03 

•45 

50-48 

51-46 

51-60 

51-56 

50-44 

43-76 

26-62 

•40 

44-80 

45-00 

45-00 

45-50 

44-80 

41-07 

26-58 

•45 

49-63 

50-33 

49-63 

52-04 

48-42 

43-29 

28-49 

•50 

54-35 

55-06 

54-96 

54-66 

53-25 

47-21 

30-00 

•60 

63-82 

65-23 

65-23 

65-23 

59-69 

53-75 

31-51 

•70 

74-09 

'  75-40 

73-79 

72-28 

64-22 

56-47 

32-92 

•80 

84-83 

87-98 

84-76 

77-61 

67-75 

58-79 

33-82 

•90 

94-72 

97-44 

94-62 

80-13 

70-56 

59-09 

34-93 

1-00 

105-49 

112-94 

104-69 

83-05 

72-38 

59-49 

36-24 

We  see  from  the  tables  that  with  a  given  spark  length  between 
two  equal  spheres,  one  charged  and  insulated  and  the  other  put  to 
earth,  the  potential  difference  varies  with  the  diameter  of  the 
spheres;  starting  with  planes  the  potential  difference  at  first 
increases  with  the  curvature  and  attains  a  maximum  when  the 
sphere  has  a  certain  diameter.  This  critical  diameter  depends 
upon  the  spark  length,  the  shorter  the  spark  the  smaller  the 
critical  diameter. 

*  Bailie,  Annales  de  Chimie  et  de  Physique  [5],  xxv.  p.  486,  1882. 
t  Paschen,  Wied.  Ann.,  xxxvii.  p.  79,  1889. 

25—2 


388  SPARK   DISCHARGE. 

B.    SHORT  SPARKS.  LONG  SPARKS. 


[11 


Spark 
Length 
in  cms. 

Spheres 
1  cm. 
radius 

Spheres 
•5  cm. 
radius 

Spheres 
•25  cm. 
radius 

•01 

3-8 

3-42 

3-61 

•02 

5-04 

5-18 

5-58 

•03 

6-62 

6-87 

6-94 

•04 

8-06 

8-82 

8-43 

•05 

9-56 

9-75 

9-86 

•06 

10-81 

10-87 

11-19 

•07 

11-78 

12-14 

12-29 

•08 

13-40 

13-59 

13-77 

•09 

14-39 

14-70 

14j89 

•10 

15-86 

15-97 

16-26 

.      -11 

16-79 

17-08 

17-26 

•12    ' 

18-28 

18-42 

18-71 

•14v 

20-52 

20-78 

21-26 

Spark 
Length 
in  cms. 

Spheres 
1  cm. 

radius 

Spheres 
•5  cm. 
radius 

Spheres 
•25  cm. 
radius 

•10 

15-96 

16-11 

16'45 

•15 

21-94 

22-17 

22-59 

•20 

27-59 

27-78 

28-18 

•25 

32-96 

33-42 

33-60 

•30 

38-59 

39-00 

38-65 

•35 

43-93 

44-32 

43-28 

•40 

49-17 

49-31 

47-64 

•45 

54-37 

54-18 

51-56 

•50 

5971 

59-03 

54-57 

•55 

64-60 

63-35 

57-27 

•60 

69-27 

67-80 

59-95 

V     -70 

'J78-51 

75-04 

63-14 

•80 

'  87-76 

81-95 

66-39 

•90 

68-65 

1-00 

; 

70-6 

1-20 

74*94 

1-50 

79-42. 

The  results  given  in  these  tables  show  that  when  the  spheres 
.are  very  small  the  potential  difference  required  to  produce  a  spark 


Fig.  112. 


197] 


SPARK   DISCHARGE. 


389 


of  given  length  is,  if  the  spark  is  not  too  short,  very  much  less 
than  the  potential  required  to  produce  the  same  length  of  spark 
between  parallel  planes,  and  that  the  spark  potential  difference 
with  points  as  electrodes  only  increases  slowly  with  the  length  of 
the  spark.  The  effect  of  the  shape  of  the  electrode  on  the  spark 
length  is  shown  by  the  curves  represented  in  Fig.  112,  which  is 
taken  from  a  paper  by  De  la  Rue  and  Miiller*.  The  curves  give 
the  relation  between .  spark  potential  and  spark  length  for  two 
planes,  two  spheres  one  3  cm.  in  radius,  the  other  1*5  cm.  in 
diameter,  two  coaxial  cylinders,  a  plane  and  a  point,  and  two 
points. 

197.  Schusterf  has  by  the  aid  of  Kirchhoff's  solution  of  the 
problem  of  the  distribution  of  electricity  over  two  spheres,  calcu- 
lated from  Bailie's  and  Paschen's  results  the  maximum  electric 
intensity  in  the  field  before  the  spark  passed:  the  results  for 
Bailie's  experiments  are  given  in  the  following  table. 


Spark 
Length 
in  cms. 

Planes 

Spheres 
6  cm. 
diam. 

Spheres 
3cm. 
diam. 

Spheres 
1cm. 
diam. 

Spheres 
•6cm. 
diam. 

Spheres 
•35  cm. 
diam. 

Spheres 
•1  cm. 
diam. 

•05 

179 

180 

186 

190 

197 

206 

292 

•10 

147 

149 

153 

163 

176 

198 

376 

•15 

135 

138 

141 

157 

170 

206 

425 

•20 

127 

131 

137 

154 

170 

219 

460 

•25 

122 

127 

134 

154 

180 

236 

478 

•30 

118 

124 

130 

156 

189 

253 

494 

•35 

116 

122 

129 

159 

197 

263 

516 

•40 

113 

122 

129 

164 

204 

272 

528 

•45 
•40 

112 

120 

127 

166 

214 

278 

540 

112 

118 

124 

157 

197 

268 

539 

•45 

110 

119 

122 

167 

206 

275 

578 

•50 

109 

117 

125 

166 

218 

296 

608 

•60 

106 

116 

125 

181 

233 

327 

639 

•70 

106 

117 

126 

188 

234 

339 

667 

•80 

106 

123 

130 

192 

250 

349 

685 

•90 

105 

120 

132 

191 

255 

349 

708 

1-00 

106 

128 

133 

194 

258 

349 

733 

It  will  be  seen  that  the  smaller  the  spheres,  i.e.  the  more 
irregular   the   electric   field,  the   greater  the   maximum   electric 


*  De  la  Rue  and  Miiller,  Phil  Tram.  1878,  Pt.  i.  p.  55. 
t  Schuster,  Phil.  Mag.,  v.  29,  p.  182,  1890. 


390  SPARK   DISCHARGE.  [197 

intensity.  We  must  be  careful  to  distinguish  between  the  electric 
field  before  the  spark  passes  and  the  electric  field  during  the 
discharge  or  even  during  the  interval  between  the  application  of 
the  potential  difference  and  the  passage  of  the  discharge,  for  during 
this  interval  ions  are  moving  about  in  the  field  and  producing 
fresh  ions ;  both  of  these  effects  will  modify  the  distribution  of  the 
electric  field.  Thus  to  take  an  example,  suppose  we  have  a  nega- 
tively electrified  point  near  to  a  positively  electrified  plate  ;  if 
there  are  no  ions  in  the  field  the  electric  force  would  be  a 
maximum  at  the  point,  and  would  steadily  diminish  as  we 
approach  the  plate ;  if,  however,  there  are  ions  present  in  the 
neighbourhood  of  the  point  the  negative  ions  will  be  repelled 
from  the  point,  while  the  positive  ions  will  be  pulled  into  it ; 
this  will  have  the  effect  of  increasing  the  electric  intensity  at 
a  distance  from  the  point  at  the  expense  of  that  close  to  the 
point :  if  the  negative  ions  congregate  at  the  plate,  so  as  to  form 
a  layer  of  negative  electrification  close  to  the  plate,  the  electric 
intensity  at  the  plate  may  rise  to  very  high  values.  This  is  what 
actually  occurs,  for  Mr  Blyth  has  measured  at  the  Cavendish 
Laboratory  the  distribution  of  electric  intensity  between  a  point 
and  a  plate  when  the  discharge  is  passing,  and  has  shown  that 
it  is  large  close  to  the  point,  is  then  comparatively  small  for 
some  distance  but  becomes  large  again  close  to  the  plate. 

The  alteration  of  the  electric  field  during  the  'lag'  will  explain 
why  a  spark  does  not  necessarily  pass  when  one  or  both  of  the 
electrodes  are  small,  even  although  the  potential  difference  between 
one  of  the  electrodes  a  and  a  point  in  the  field  P  near  to  A 
(calculated  on  the  assumption  that  there  are  no  ions  in  the  field) 
is  greater  than  that  required  to  produce  a  spark  of  length  aP 
between  plane  electrodes,  for  during  the  'lag'  the  movement  of 
the  ions  in  the  field  may  have  so  reduced  the  potential  difference 
between  a  and  P  that  it  is  less  than  that  required  to  produce 
a  spark  of  length  aP. 

Although  the  processes  going  on  during  the  lag  may  reduce  the 
inequalities  in  the  electric  field  between  small  electrodes  they 
cannot  be  expected  to  remove  them  entirely,  and  when  the  field  is 
far  from  uniform,  as  is  the  case  with  pointed  electrodes,  we  can 
easily  see  that  the  potential  difference  required  to  produce  a  long 
spark  is  less  than  that  required  to  produce  a  spark  of  the  same 


198] 


SPARK  DISCHARGE. 


391 


length  between  plane  electrodes.  For  let  the  curve  APQ  (Fig. 
113)  represent  the  distribution  of  potential  between  small  elec- 
trodes AB,  and  let  CD  be  the  curve  which  represents  the  potential 


Fig.  113. 

difference  required  to  produce  a  spark  in  a  uniform  field  (the 
ordinate  of  a  point  on  CD  represents  the  spark  potential  required 
to  produce  a  spark  whose  length  is  equal  to  the  abscissa  of  the 
point);  then  we  see  that  although  the  potential  difference  BQ 
between  the  small  electrodes  may  be  less  than  BD,  that  required 
to  produce  a  spark  of  length  AB  in  a  uniform  field,  the  two  curves 
may  intersect ;  if  they  do  so  at  P,  then  a  spark  will  pass  from 
A  to  P,  the  whole  potential  difference  will  be  thrown  on  the 
region  between  P  and  B,  so  that  the  strength  of  this  part  of  the 
field  will  increase  and  the  spark  will  travel  on  to  B. 

198.  When  the  electrodes  are  of  different  sizes  Faraday* 
found  that  the  spark  potential  is  different  according  as  the  smaller 
electrode  is  positive  or  negative ;  De  la  Rue  and  Mtillerf  also 
observed  the  same  effect;  according  to  WesendonckJ  this  differ- 
ence only  occurs  when  a  brush  discharge  accompanies  the  spark, 
when  the  conditions  are  such  that  the  discharge  passes  entirely 
as  a  spark  the  spark  potential  is  the  same  whichever  way  the  spark 
passes. 

*  Faraday,  Experimental  Researclies,  §  1480. 

t  De  la  Rue  and  Muller,  Phil.  Trans.,  1878,  Pt.  i.  p.  55. 

J  Wesendonck,  Wied.  Ann.,  xxviii.  p.  222. 


392  SPARK   DISCHARGE.  [199 


Pressure  in  the  Spark. 

199.  The  ions  in  the  electric  field  acquire  kinetic  energy  and 
as  the  pressure  in  a  gas  is  proportional  to  the  kinetic  energy 
per  unit  volume  the  pressure  along  the  path  of  the  spark  will  be 
increased.  This  increase  in  pressure  may  be  very  large  ;  for  it  is 
easy  to  show  that  the  kinetic  energy  given  to  the  ions,  when  a 
quantity  of  electricity  equal  to  Q  passes  through  the  spark,  is  equal 
to  VQ,  where  V  is  the  spark  potential.  To  take  an  example,  let 
us  suppose  that  we  have  a  spark  one  cm.  long  through  air  at  atmo- 
spheric pressure,  and  that  we  discharge  by  this  spark  the  charge 
in  a  condenser  of  1000  cm.  capacity  charged  to  the  potential 
difference  required  to  produce  the  spark,  this  potential  difference 
is  about  30000  volts,  i.e.  100  in  electrostatic  units,  hence  in  this 
case  F=102  and  Q  =  102  x  103,  thus  the  energy  given  to  the  gas 
is  107  ergs.  Now  if  this  energy  were  distributed  throughout  1  c.c. 
of  gas  it  would  increase  the  pressure  by  6'6  atmospheres,  it  is 
however  confined  to  the  very  much  smaller  volume  traversed  by 
the  spark,  the  pressure  in  this  region  will  be  proportionately 
greater  ;  to  take  -^  of  a  c.c.  as  the  volume  of  gas  traversed  by 
the  spark  would  probably  be  a  very  large  over-estimate,  and  yet 
even  if  the  volume  were  no  less  than  this  the  initial  pressure 
along  the  path  of  the  spark  would  be  660  atmospheres.  This 
high  pressure  would  spread  as  a  pulse  from  the  region  of  the 
spark-gap,  the  pressure  in  the  pulse,  when  this  had  got  so  far 
from  the  spark-gap  that  it  might  be  regarded  as  spherical, 
varying  inversely  as  the  square  of  the  distance  from  the  spark  - 


A  well-known  instance  of  the  effects  produced  by  this  pressure 
is  what  is  called  the  '  electrical  bomb/  where  a  loosely-fitting  plug 
in  a  closed  vessel  is  blown  out  when  a  spark  passes  through  the 
vessel.  The  effect  can  easily  be  observed  if  a  pressure-gauge,  in 
which  the  pressure  is  indicated  by  the  motion  of  a  small  quantity 
of  a  light  liquid,  is  attached  to  an  ordinary  discharge-tube,  the 
pressure  in  the  gas  being  most  conveniently  from  2  to  10  mm. 
of  mercury.  At  the  passage  of  each  spark  there  is  a  quick  move- 
ment of  the  liquid  in  the  gauge  as  if  it  had  been  struck  by  a  blow 
coming  from  the  tube  ;  immediately  after  the  passage  of  the  spark 


199]  SPARK  DISCHARGE.  393 

the  liquid  in  the  gauge  springs  back  within  a  short  distance  of  its 
position  of  equilibrium  and  then  slowly  creeps  back  the  rest  of  the 
way.  This  latter  effect  is  probably  due  to  the  slow  escape  of  the 
heat  produced  by  the  passage  of  the  spark,  the  gauge  behaves 
just  as  it  would  if  a  wave  of  high  pressure  rushed  through  the 
gas  when  the  spark  passed.  The  increased  pressure  due  to  the 
discharge  has  been  described  by  Meissner*  and  by  De  la  Rue 
and  Miillerf. 

The  existence  of  a  pulse  spreading  from  the  spark  has  been 
beautifully  demonstrated  by  ToplerJ  who  studied  by  the  method 
of  instantaneous  illumination  the  region  round  the  spark  imme- 
diately after  it  had  passed.  As  the  density  of  the  air  in  the  pulse 
differs  from  that  of  the  surrounding  gas,  the  pulse  is  optically 
different  from  the  rest  of  the  field  and  so  can  be  made  visible. 
Fig.  114  a,  taken  from  Topler's  paper,  represents  the  appearance 


Fig.  114. 

of  the  field  looking  so  as  to  see  the  whole  length  of  the  spark, 
Fig.  114  6  the  appearance  when  the  spark  is  looked  at  end-on. 

Tb'pler  noticed  that  the  initial  disturbance  close  to  the  spark 
gap  showed  periodic  expansions  and  contractions,  as  if  the  regions 
of  greatest  disturbance  were  distributed  at  equal  intervals  along 
the  length  of  the  spark.  There  was  an  exceptionally  large  pro- 
tuberance in  the  neighbourhood  of  the  cathode. 


*  Meissner,  Abhand.  der  kimig.  Geselhchaft  Gottingen,  xvi.  p.  98,  1871. 

t  De  la  Rue  and  Miiller,  Phil.  Trans.,  1880,  p.  86. 

£  Topler,  Pogg.  Ann.,  cxxxi.  pp.  33,  180,  1867 ;  cxxxiv.  p.  194,  1868. 


394  SPARK  DISCHARGE.  [199 

In  an  experiment  due  to  Hertz  which  also  illustrates  well 
the  explosive  effects  due  to  the  spark  the  explosion  seemed  to  be 
more  vigorous  at  the  anode  than  at  the  cathode*;  in  this  experi- 
ment the  anode  was  placed  at  the  bottom  of  a  glass  tube  with 
a  narrow  mouth,  while  the  cathode  was  placed  outside  the  tube 
and  close  to  the  open  end.  The  tube  and  the  electrodes  -were  in 
a  bell-jar  filled  with  dry  air  at  a  pressure  of  40 — 50  mm.  of 
mercury.  When  the  discharge  from  a  Leyden  jar  charged  by 
an  induction  coil  passed  through  the  tube,  the  glow  accompanying 
the  discharge  was  blown  out  of  the  tube  and  extended  several 
centimetres  from  the  open  end;  the  effect  was  not  so  marked  when 
the  electrodes  were  reversed. 

Haschek  and  Machef  by  measuring  the  pressure  at  the  surface 
of  a  vessel  through  which  sparks  from  a  high  tension  transformer 
were  passing  have  calculated  the  pressure  in  the  spark ;  with  brass 
electrodes  amj  sparks  3  mm.  long  they  estimated  the  pressure  of 
the  spark  in  air  at  a  pressure  of  704  mm.  of  mercury'as  51*7  atmo- 
spheres, in  carbonic  acid  at  the  same  pressure  52*2  atmospheres, 
and  in  coal  gas  as  72'7  atmospheres ;  they  found  that  the  pressure 
in  the  spark  was,  as  might  be  expected  from  the  diminution  in 
the  spark  potential,  less  wheijjtfthe  pressure  of  the  gas  through 
which  the  spark  passed  was*  low  than  when  it  was  high  :  thus  in 
one  of  their  experiments  Jftie  pressure  in  the  spark  was  estimated 
by  them  to  be  27 '2  atmospheres  when  the  pressure  of  the  air  was 
585  mm.  of  mercury,  when  the  air  pressure  was  reduced  to  96  mm. 
of  mercury  the  spark  pressure  fell  to  one  atmosphere.  They  found 
too  that  the  spark  pressure  depended  upon  the  nature  of  the 
electrodes;  thus  under  similar  conditions  they  found  that  the 
spark  pressures  in  air  with  electrodes  of  carbon,  iron  and  brass 
were  respectively  124,  79,  64  atmospheres.  When  as  in  these 
experiments  sparks  follow  each  other  in  rapid  succession,  the  spark 
is  carried  to  a  considerable  extent  by  the  metallic  vapour  from  the 
electrode. 

Haschek  and  Exner J  and  Mohler§  have  published  estimates  of 

the  spark  pressure  derived  from  observations  of  the  displacement 

• 

*  Hertz,  Wied.  Ann.,  xix.*p.  87,  1893. 
t  Haschek  and  Mache,  Wied.  Ann.,  Ixviii.  p.  740,  1899. 
£  Haschek  and  Exner,  Wien.  Sitzungs.,  cvi.  p.  1127,  1897. 
§  Mohler,  Astrophysical  Journal,  iv.  p.  175,  1896. 


200]  SPARK   DISCHARGE.  395 

of  the  lines  in  the  spectrum  of  the  spark  due  to  the  electrode. 
Humphreys*  has  shown  that  the  effect  of  increased  pressure  in 
the  vapour  of  a  metal  is  to  displace  the  lines  towards  the  red  end 
of  the  spectrum,  and  has  measured  the.  displacement  for  various 
pressures ;  hence  if  we  assume  that  the  displacement  of  the  lines 
in  the  spark  spectrum  is  due  to  the  pressure  of  the  spark,  if  we 
measure  this  displacement  we  can  deduce  the  pressure  in  the  spark. 

The  magnitude  of  the  pressures  in  the  spark  explains  the 
mechanical  effects  produced  by  sparks,  such  as  the  perforation  of 
pieces  of  cardboard  or  thin  plates  of  glass. 

Heating  Effects  produced  by  Sparks. 

200.  A  large  part  of  the  energy  given  to  the  ions  during 
the  discharge  will  appear  as  heat  and  will  raise  the  tempera- 
ture of  the  gas  and  the  vessel  in  which  it  is  contained. 
Measurements  of  the  heat  produced  by  sparks  have  been  made 
by  Riessf,  PaalzowJ,  G.  Wiedemann§,  Naccari  and  Bellati||,  Pog- 
gendorfff,  Dewar**,  Rollmannff,  Naccarift,  Villari§§,  Mugna|||| : 
measurements  in  absolute  measure  have  been  made  by  Heyd- 
willerTfl  and  Kauffmann***.  These  experiments  have  mostly 
been  made  on  the  heat  developed  by  the  sparks  produced  by 
discharging  Leyden  jars ;  the  most  'definite  result  obtained  is  that- 
the  heat  produced  in  the  spark  ga^  is  only  a  small  fraction  of 
the  energy  in  the  jar  before  it  was  discharged.  The  discharge  of 
the  jar  is  oscillatory,  so  that  in  this  case  we  have  a  series  of 
sparks  following  one  another  across  the  gap  in  quick  succession ; 
under  these  circumstances  there  is  a  great  tendency  for  the  spark 
to  change  into  an  arc,  and  in  the  arc  the  potential  difference 

*  Humphreys,  Astrophysical  Journal,  vi.  p.  169,  1897. 

f  Eiess,  Eeibungselektricitdt. 

J  Paalzow,  Pogg.  Ann.,  cxxvii.  p.  126,  1866. 

§  G.  Wiedemann,  Pogg.  Ann.,  clviii.  p.  35,  1876. 
||  Naccari  and  Bellati,  Beib.,  ii.  p.  720,  1878. 

IT  Poggendorff,  Pogg.  Ann.,  xciv.  p.  632,  1855. 
**  Dewar,  Proc.  Roy.  Soc.  Edin.,  vii.  p.  699,  1872. 
ft  Kollmann,  Pogg.  Ann.,  cxxxiv.  p.  605,  1868. 
JJ  Naccari,  Att.  di  Torino,  xvii.  p.  1,  1882. 

§§  Villari,  Beib.,  iii.  p.  713  ;  iv.  p.-404;  v.  p.  460;  vi.  p.  699 ;  vii.  p.  782. 

Ill)  Mugna,  Beib.,  vi.  p.  953. 

1H1  Heydwiller,  Wied.  Ann.,  xliii.  p.  310,  1891 ;  Ixi.  p.  541,  1897. 
***  Kauffmann,  Wied.  Ann.,  Ix.  p.  653,  1897. 


396  SPARK   DISCHARGE.  [201 

between  the  electrodes,  and  therefore  the  heat  produced  by  a 
given  current,  is  very  much  less  than  for  the  spark.  The  relation 
between  the  electromotive  force  and  the  current  in  the  case  of  the 
discharge  through  gases  is  in  general  so  different  from  that  for 
metals  that  it  is  somewhat  misleading  to  speak  of  the  resistance 
of  the  spark  gap :  it  may,  however,  give  some  idea  of  the  small 
amount  of  energy  dissipated  in  the  spark  gap  to  say  that  the 
heating  effect  for  sparks  six  millimetres  long  has  been  found  in 
some  cases  investigated  by  Miss  Brooks*  to  be  not  greater  than 
that  which  would  have  occurred  if  a  wire  about  2  ohms  resist- 
ance occupied  the  position  of  the  spark. 

201.  Schuster  and  Hemsalechf  have  made  some  very  interest- 
ing researches  on  the  constitution  of  sparks  following  rapidly  one 
after  another,  such  as  are  produced  by  the  oscillatory  discharge  of 
a  Leyden  jar.  The  sparks  were  photographed  on  a  rapidly  moving 
film  mounted  on  the  rim  of  a  wheel  making  about  30  revolutions 
per  second,  the  motion  of  the  film  was  at  right  angles  to  the  length 
of  the  spark,  so  that  the  line  traced  on  the  film  by  a  source  of 
light  moving  with  finite  velocity  along  the  spark  length  would  be 
inclined  to  the  direction  of  the  spark,  and  its  inclination  would 
(if  the  velocity  of  the  film  were  known)  give  the  velocity  of  the 
source  of  light.  By  sending  the  light  from  the  spark  on  its  way 
to  the  film  through  a  spectroscope  the  velocity  corresponding  to 
any  line  in  the  spectrum  could  be  determined. 

The  conclusion  arrived  at  by  the  authors  from  these  experi- 
ments is  that  the  first  spark  passes  through  air,  but  that  if  the 
sparks  follow  each  other  in  rapid  succession  (as  they  do  when  pro- 
duced by  the  oscillatory  discharge  of  a  Leyden  jar)  and  are  not 
too  long  the  succeeding  ones  pass  through  the  vapour  of  metal,  the 
electrodes  being  vaporised  by  the  heat  produced  by  the  first  spark. 
This  view  is  confirmed  by  a  very  interesting  experiment  made  by 
the  authors :  they  found  that  if  self-induction  was  put  into  the 
spark  circuit  by  which  the  jars  were  discharged  the  air  lines  almost 
disappeared  from  the  spectrum  of  the  spark  while  the  metal  lines 
were  very  bright:  the  self-induction  increases  the  time  the  oscilla- 
tions last  and  so  enables  the  vapour  of  the  metal  to  get  well  diffused 

*  Miss  Brooks,  Phil.  Mag.,  vi.  2,  p.  92,  1901. 

t  Schuster  and  Hemsalech,  Phil   Trans.  1899,  vol.  cxciii.  p.  189. 


202]  SPARK   DISCHARGE.  397 

through  the  spark  gap,  the  discharge  passing  for  by  far  the  greater 
part  of  the  time  through  the  vapour  so  that  most  of  the  energy  is 
spent  in  heating  this  and  not  the  air. 

The  authors  found  that  the  velocity  of  the  metallic  vapours  in 
the  spark  was  greater  for  the  metals  of  low  atomic  weight  than 
for  those  of  high ;  thus  the  velocity  of  aluminum  vapour  was  1890 
metres  per  second,  that  of  zinc  and  cadmium  only  about  545. 

The  very  interesting  result  was  obtained  that  the  velocities 
of  the  vapours  of  some  metals  and  especially  of  bismuth  indicated 
by  some  of  the  lines  in  the  spectrum  were  not  the  same  as  those 
indicated  by  other  lines,  thus  in  bismuth  some  of  the  lines  indi- 
cated a  velocity  of  1420  metres  per  second,  others  a  velocity  of  only 
about  550,  while  one  line  (X  =  3793)  gave  a  still  smaller  velocity. 
This  result  raises  some  very  interesting  questions,  as  for  instance 
whether  bismuth  is  a  mixture  of  different  elements,  some  of  the 
lines  in  the  spectrum  being  due  to  one  constituent,  others  to  the 
other  constituents ;  ano.ther  possibility  is  that  the  molecules  even 
of  an  element  are  not  all  of  the  same  kind,  and  that  the  different 
lines  in  the  spectrum  are  emitted  by  molecules  of  different  kinds ; 
we  should  also  get  a  similar  effect  if  the  relative  intensities  of 
the  lines  varied  greatly  with  the  kinetic  energy  possessed  by  a 
molecule,  if  for  example  the  intensity  of  a  line  a  was  very  much 
greater  than  that  of  a  line  /3,  for  a  rapidly  moving  molecule,  and 
very  much  less  for  a  slowly  moving  one,  then,  if  the  molecules  of 
the  vapour  were  projected  with  different  velocities,  the  line  a  would 
indicate  a  higher  velocity  than  ft ;  on  these  points  Schuster  and 
Hemsalech  reserve  their  opinion  until  they  have  made  further 
experiments. 

Effect  of  a  Magnetic  Field  on  the  Spark. 

202.  We  shall  see  later  on  that  a  magnetic  field  produces  a 
very  great  effect  on  the  discharge  through  gases  when  the  pressure 
is  low.  At  atmospheric  pressure,  however,  the  effects  on  the  spark 
itself  are  very  slight,  although  the  halo  of  luminous  gas  which 
surrounds  the  course  of  the  sparks  when  a  number  of  sparks 
follow  each  other  in  rapid  succession  is  drawn  out  into  a  broad 
band  by  the  magnetic  field.  This  halo,  it  may  be  observed,  is 
deflected  by  a  current  of  air  though  the  spark  itself  is  not  affected. 


398  SPARK   DISCHARGE.  [203 

Precht*  has  observed  a  distinct  effect  of  a  magnet  on  a  spark  at 
atmospheric  pressure  when  the  sparks  pass  between  a  sharp  point 
and  a  blunt  wire  ;  the  spark  is  deflected  by  a  transverse  magnetic 
field  in  the  same  direction  as  a  flexible  wire  conveying  a  current 
in  the  same  direction  as  that  passing  through  a  spark  would  be 
deflected.  He  found,  too,  that  the  magnetic  field  affected  the 
spark  potential;  thus  when  the  distance  between  the  electrodes 
was  8  mm.  and  the  transverse  magnetic  force  7017  he  found  that 
when  the  pointed  electrode  was  the  anode,  the  rounded  one  the 
cathode,  the  magnetic  field  reduced  the  spark  potential  from  8670 
volts  to  7520  volts,  while  when  the  point  was  cathode,  the  rounded 
electrode  anode  the  same  magnetic  field  increased  the  potential 
from  6250  to  6450  volts. 

Appearance  of  Long  Sparks. 

«» 

203.     When  sparks  are  of  considerable  length  they  exhibit  a 
branched  appearance,  as  shown  in  Fig.  115,  the  branches  pointing 


Fig.  115. 

to  the  negative  electrode ;  the  electricity  flowing  along  those 
branches  which  terminate  abruptly  must  ultimately  find  its  way  to 
the  electrodes  by  a  dark  discharge.  The  appearance  of  the  spark 
is  different  at  the  positive  and  negative  terminals,  there  is  a  single 
straight  stem  at  the  positive,  while  at  the  negative  the  discharge 
is  divided  into  several  threads.  The  spark  along  its  course 
exhibits  abrupt  changes  in  direction  as  if  it  made  its  way  by 
a  series  of  jumps  rather  than  as  an  uninterrupted  stream. 

*  Precht,  Wied.  Ann.,  Ixvi.  p.  676,  1896. 


205]  SPARK   DISCHARGE.  399 


Discharge  of  Electricity  from  Points. 

204.  A  very  interesting  case  of  electric  discharge  is  that 
between  a  sharply  pointed  electrode,  such  as  a  needle,  and  a  neigh- 
bouring metallic  electrode  of  considerable  area.  In  this  case  the 
luminosity  is  confined  at  atmospheric  pressure  to  the  neighbourhood 
of  the  electrode,  the  current  through  the  rest  of  the  gas  is  carried 
almost  entirely  by  ions  of  the  same  sign  as  the  charge  on  the  point. 

Chattock  (see  page  53)  has  shown  that  the  velocity  of  these 
ions  under  unit  electric  force  is  the  same  as  that  of  the  ions  pro- 
duced by  Rontgen  or  Becquerel  rays,  and  Townsend  (see  page  29) 
has  shown  that  the  charge  on  the  ions  is  also  the  same.  If  the 
point  is  placed  at  right  angles  to  a  large  metal  plane,  then  for 
electricity  to  stream  from  the  point  the  potential  of  the  point 
must  exceed^ that  of  the  plane  by  an  amount  called  by  v.  Rontgen  * 
the  minimum  potential ;  this  minimum  potential  depends  upon 
the  sharpness  of  the  point,  the  pressure  and  nature  of  the  gas  and 
the  sign  of  the  electrification  of  the  point,  being  less  if  the  point 
is  negatively  than  if  it  is  positively  electrified ;  according  to  War- 
burg f,  the  minimum  potential  does  not  depend  upon  the  distance 
of  the  point  from  the  plane.  When  the  potential  difference  be- 
tween the  point  and  the  plane  exceeds  the  *  minimum  potential ' 
a  current  of  electricity  passes  from  the  point  to  the  plane;  the 
magnitude  of  this  current  for  a  given  potential  difference  between 
the  point  and  the  plane  rapidly  diminishes  as  the  distance  from 
the  plane  increases:  Warburg  (I.e.)  has  shown  that  if  d  is  the 
shortest  distance  between  the  point  and  the  plane,  then  for  a  given 
difference  of  potential  the  current  is  proportional  to  I/d3'17,  this 
law  holds  whatever  be  the  sharpness  of  the  point. 


Value  of  the  Minimum  Potential. 

205.  As  this  depends  upon  the  sharpness  of  the  point  we  can 
only  compare  the  values  of  this  quantity  for  the  same  point  under 
different  circumstances.  The  following  table  gives  the  value  for 

*  v.  Rontgen,  Gottingen.  Nach.  p.  390,  1878. 
t  Warburg,  Wied.  Ann.,  Ixvii.  p.  69,  1899. 


400 


SPARK  DISCHARGE. 


[205 


the  minimum  potential  with  the  same  point  at  different  pressures 
as  determined  by  Tamm*  : 


Pressure  in  cm.  of  mercury 

Point  - 

Point  + 

76 

2140  volts 

3760  volts 

70 

2135 

3755 

60 

2105 

3705 

50 

2035 

3585 

40 

1905 

3350 

30 

1690 

2970 

20 

1360 

2390 

10 

910 

1580 

Thus  the  change  in  the  minimum  potential  with  the  pressure 
is  very  slow  when  the  pressures  are  high  but  becomes  much  faster 
at  lower  pressures. 

The  ratio  of  the  minimum  potential  for  positive  and  negative 
points  is  approximately  the  same  at  all  pressures.  Observations 
of  the  minimum  potential  in  different  gases  have  been  made  by 
v.  Rontgen  f  and  by  Precht J;  the  results  of  their  observations  are 
given  in  the  following  table,  the  numbers  in  the  first  two  columns 
are  due  to  v.  Rontgen,  those  in  the  third  and  fourth  to  Precht. 


Minimum  potential,  point  + 

Minimum  potential,  pressure 
760  mm. 

Gas 

Pressure  205  mm. 

Pressure  110  mm. 

Point  + 

Point  - 

H2      .... 

1296  volts 

1174  volts 

2125  volts 

1550  volts 

02      .... 
CO     .... 

2402     „ 
2634     „ 

1975     „ 
2100     „ 

2800     „ 

2350     „ 

CH4  .... 

2777     „ 

2317     „ 

NO    .... 

3188     „ 

2543     „ 

C02  .... 

3287     „ 

2655     „ 

3475     „ 

2100     „ 

N2     .... 

2600     „ 

2000     „ 

Air    .... 

2750     „ 

2050     „ 

*  Tamm,  Drude's  Ann.,  vi.  p.  259,  1901. 

t  v.  Rontgen,  Gottingen.  Nach.,  1878,  p.  390. 

J  Precht,  Wied.  Ann.,  xlix.  p.  150,  1893. 


206]  SPARK   DISCHARGE.  401 


Connection  between  Potential  Difference  and  Current. 

206.  Warburg  (I.e.)  found  that  using  the  same  point  and  keep- 
ing it  at  the  same  distance  from  the  plate  the  relation  between 
the  current  i  and  the  potential  V  can  be  expressed  by  the  relation 


where  M  is  the  minimum  potential.  Sieveking*  considered  that 
the  linear  relation  i  =  b  (  V  —  M)  represented  his  experiments  with 
sufficient  accuracy:  in  a  recent  paper  by  Tammf  this  question  is 
discussed,  and  a  formula  of  the  type  of  Warburg  shown  to  give 
better  agreement:  in  place  of  the  minimum  potential  M  Tamm 
writes  J  (Ml  +  M^)  where  M1  is  the  potential  at  which  the  discharge 
begins  when  the  potential  is  gradually  increased,  M2  that  at  which 
it  leaves  off  when  it  is  gradually  lowered,  the  two  are  not  identical 
the  latter  being  the  smaller :  the  application  of  the  formula  in 
this  form  is  limited  to  potential  differences  considerably  greater 
than  M. 

The  current  with  the  same  potential  difference  increases  as  the 
pressure  diminishes,  this  is  shown  by  the  following  results  due  to 
Tamm  (1.  c.).  (See  Tables,  p.  402.) 

It  will  be  noticed  that  the  current  with  the  point  positive  is 
always  less  than  that  with  the  point  negative,  the  potential  differ- 
ence being  the  same  in  the  two  cases.  The  increase  of  the  current 
as  the  pressure  diminishes  is  more  rapid  at  small  pressures  than 
at  high  pressures ;  the  current  seems  to  be  roughly  proportional 
to  the  reciprocal  of  the  pressure,  while  at  low  pressures  it  varies 
as  the  square  of  this  quantity. 

Tamm  gives  as  the  relation  between  ix  the  current  at  a  pres- 
sure of  x  centimetres,  and  i78  the  current  at  76  cm.  pressure,  the 
potential  difference  being  V  in  both  cases,  the  empirical  equation 

76        3/T ,      76 


*  Sieveking,  Drude's  Ann.,  i.  p.  299,  1900. 
t  Tamm,  Drude's  Ann.,  vi.  p.  259,  1901. 
T.  G.  26 


402 


SPARK   DISCHARGE. 


[207 


Current  in  micro-amperes. 


Potential  difference... 
Pressure 

-4000 

-6000 

-8000 

-10000 

76 

1-4 

4-2 

8-0 

13'4 

70 

1-6 

4-6 

8-6 

14-5 

60 

2-0 

57 

10-5 

17-6 

50 

2-6 

7-8 

13-7 

22-8 

40 

3-7 

11-3 

20-4 

33-7 

30 

6-8 

19-5 

35'3 

58-0 

20 

14-6 

44.7 

80-9 

134-2 

Potential  difference... 

+  4000 

+  6000 

+  8000 

+  10000 

Pressure  in  cm.  of  Hg. 

76 

0-7 

2-1 

4-8 

9-3 

70 

0-8 

2-3 

51 

10-1 

60 

1-0 

2-8 

6-3 

12-3 

50 

1-3 

3-8 

8'2 

16-0 

40 

1-9 

5-6 

12-3 

23-5 

30 

3-3 

9-7 

21-1 

40-4 

20 

7-3 

224 

48-0 

93-0 

207.  Warburg*  has  shown  that  the  presence  of  minute  traces 
of  oxygen  in  gases  such  as  hydrogen  or  nitrogen  produces  a  great 
diminution  in  the  current  from  a  negative  point  while  it  has  but 
little  effect  on  that  from  a  positive  one  ;  thus  the  removal  of  a  trace 
of  oxygen  from  nitrogen  increased  the  current  from  a  negative  point 
in  that  gas  fifty  times  ;  this  may  be  taken  as  indicating  that 
oxygen  has  a  great  tendency  to  collect  round  the  carriers  of  the 
negative  charge  and  either  make  them  less  efficient  as  ionisers  or 
else  make  them  move  more  slowly  in  the  electric  field. 


208.  Warburgf  ^as  investigated  the  proportion  of  current 
received  at  different  portions  of  the  plane  opposite  the  electrified 
point  ;  he  finds  that  the  amount  received  per  unit  area  at  a  point 
Q  on  the  plane  is  proportional  to  cosm  6  where  6  is  the  angle  QPO, 
P  being  the  electrified  point  and  0  the  normal  from  P  on  the 

*  Warburg,  Drude's  Ann.,  ii.  p.  295,  1900. 
t  Warburg,  Wied.  Ann.,  Ixvii.  p.  69,  1899. 


209]  SPARK   DISCHARGE.  403 

plane,  the  electrified  conductor  is  supposed  to  be  at  right  angles 
to  the  plane ;  he  finds  that  m  for  a  negatively  electrified  point  is 
equal  to  4*65,  for  a  positively  electrified  point  4*82,  and  that  it  is 
independent  of  the  sharpness  of  the  point. 

The  Electrical  Wind. 

209.  The  current  of  electrified  ions  which  constitutes  the  dis- 
charge from  the  point  sets  the  air  in  the  neighbourhood  in  motion. 
For  when  the  ions  have  settled  down  into  the  state  in  which  their 
velocity  is  proportional  to  the  electric  force  acting  upon  them 
the  mechanical  force  acting  upon  them  is  transferred  to  the  air 
through  which  they  are  moving,  this  gives  rise  to  currents  of  air 
directed  from  the  point,  and  these  air  currents  are  what  is  known 
as  the  electrical  wind.  This  motion  of  the  air  forwards  is  accom- 
panied by  a  reaction  on  the  point,  tending  to  drive  it  backwards. 
This  reaction  has  been  measured  by  Arrhenius*,  who  finds  that 
when  positive  electricity  is  escaping  from  a  point  into  air  the 
reaction  tending  to  drive  the  point  backwards  is,  when  the 
current  is  kept  constant,  proportional  to  the  pressure  of  the  gas, 
and  for  different  gases  at  the  same  pressure  (air,  hydrogen,  and 
carbonic  acid)  varies  as  the  square  root  of  the  molecular  weight 
of  the  gas.  The  reaction  when  an  equal  current  of  negative 
electricity  is  escaping  from  the  point  is  much  less,  the  proportion 
between  the  two  depending  on  the  pressure  of  the  gas;  thus  in  air 
at  a  pressure  of  70  cm.  the  reaction  on  the  positive  point  was 
1*9  times  that  of  the  negative,  at  40  cm.  2*6  times,  at  20  cm.  3'2 
times,  at  10'3  cm.  7  times,  and  at  5'1  cm.  15  times  the  reaction  of 
the  negative  point.  The  reaction  on  the  discharging  point  is  due 
to  the  repulsion  between  the  electrified  point  and  the  ions  carry- 
ing the  discharge  ;  we  can  easily  calculate  this  force.  Suppose  that 
the  needle  from  which  the  electricity  is  discharged  points  in  the 
direction  of  the  axis  of  z ;  let  p  be  the  density  of  the  ions  at  any 
part  of  the  field,  Z  the  electric  force  at  the  same  point,  then  F, 
the  force  parallel  to  z  acting  on  the  ions,  is  equal  to 

jjjZpdxdydz ; 

I  but  if  w  is  the  velocity  of  the  ion  parallel  to  z,  w  =  kZ  where  k  is 

I  ,    - 

*  Arrhenius,  Wied.  Ann.,  Ixiii.  p.  305,  1897. 

26—2 


404  SPARK   DISCHARGE.  [209 

the  velocity  of  the  ion  under  unit  electric  force  ;  substituting  this 
value  for  Z  we  get 

F=  I     j  pdxdydz] 

but  if  i  is  the  current 

i  —  jjwpdxdy, 

hence  if  k  is  constant  throughout  the  field 


(1). 


The  reaction  on  the  point  is  equal  to  F,  hence  for  a  constant 

current  F  varies  inversely  as  k  ;  this  conclusion  agrees  when  the 

point  is  positively  electrified  with  the  results  of  Arrhenius's  experi- 

ments.    For  let  us  first  consider  the  effects  of  pressure,  k  varies 

inversely  as  the  pressure  ;  hence  F  should  be  directly  proportional 

to   the   pressure,  this  is  in   agreement   with  Arrhenius's   result  ; 

next  consider  the  reaction  of  different  gases,  if  we  refer  to  the 

values  given  on  page  56,  we  see  that  the  velocities  of  the  ions 

under  unit  electric  force  are  roughly  inversely  proportional  to  the 

square  roots  of  the  densities  of  the  gases,  hence  F  should  be  approxi- 

mately directly  proportional  to  the  square  roots  of  these  densities. 

Since  the  velocity  of  the  negative  ion  is  greater  than  that  of  the 

positive  the  reaction  on  the  negative  point  should  be  less  than 

that  on  the  positive;   the  ratio  of  the  reaction  on  the  positive 

point  to  that  on  the  negative  is  however  much  greater  than  the 

ratio  of  the  velocity  of  the  negative  ion  to  that  of  the  positive. 

We  have  seen  however  reasons  for  believing  that  a  rapid  con- 

densation of  the  gas  takes  place  around  the  newly-formed  negative 

ions  after  they  are  produced  at  the  point,  so  that  the  velocity  of 

the  negative  ion  will  be  greater  at  first  than  after  it  has  been  for 

some  time  in  the  gas,  it  is  only  however  for  these  aged  ions  that 

we  know  the  velocity,  while  in  the  case  of  the  point  discharge  a 

large  part  of  the  reaction  will  be  due  to  the  more  rapidly  moving 

freshly-formed  ions  in  the  immediate  neighbourhood  of  the  point, 

so  that  the  value  of  F  will  be  less  than  that  determined  by  equa- 

tion (1)  when  we  substitute  for  k  the  observed  velocity  of  the 

negative  ion. 


211]  SPARK   DISCHARGE.  405 

Discharge  from  a  point  whose  electrification  is  rapidly 
changing  sign. 

210.  If  a  point  is  charged  up  to  a  high  and  rapidly  alternating 
potential,  such  as  can  be  produced  by  the  electrical  oscillations 
started    when    a   Leyden-jar    is   discharged,   then    in    hydrogen, 
nitrogen,  ammonia,  and  carbonic  acid  gas,  a  conductor  placed  near 
the   point   gets  a  negative,   while  in  air  and  oxygen  it  gets  a 
positive  charge*.     Himstedtf  has  shown  that  the  distribution  of 
electrification  in  these  gases  differs  only  in  degree;  he  finds  that  in 
air  and  oxygen,  although  the  electrification  is  positive  near  the 
point,  yet  it  changes  sign  as  we  recede  from  it  and  ultimately 
becomes    negative ;     while    in    hydrogen    and    the    other   gases 
mentioned   above    we  get  positive   electrification  if  we  go  close 
up  to  the  point;    the   difference   between   the   gases  is  that  in 
air    the    place   where   the    electrification    changes   sign   is    some 
distance  from  the  point,  while  in  hydrogen  it  is  close  up  to  it. 
This   outer   zone    of  negative   electrification  is  what   we  should 
expect  from  the  greater  velocity  of  the  negative  ions,  for  under  an 
alternating  electric  field  the  amplitude  of  the  path  of  the  faster 
ions   would  be  greater  than  that  of  the  slower,  and  thus  at  a 
distance  from  the  point  greater  than  the  amplitude  of  the  slower 
ions  there  would  be  nothing  but  negative   electricity.     The   de- 
termination of  the  distance  at  which  the  electrification  changes 
sign  would  be  a  very  complicated  investigation,  as  it  would  involve 
in  addition  to  the  relative  velocities  of  the  positive  and  negative  ions 
the  difference  in  the  values  of  the  current  proceeding  from  the  point 
according  as  it  is  positively  or  negatively  electrified,  as  well  as  the 
difference  in  the  minimum  potential  at  which  the  discharge  begins. 

211.  The  condition  of  a  point  from  which  electricity  is  discharg- 
ing seems  to  suffer  some  modification  as  the  discharge  goes  on,  and 
this  gives  rise  to  variations  in  the  current:  PrechtJ  found  that  a 
point  from  which  positive  electricity  had  been  discharged  some- 
times got  hollowed  out  into  a  kind  of  crater,  as  if  some  of  the 
metal  had  been  torn  away ;  he  found  that  a  negatively  electrified 
point  did  not  suffer  any  change  of  shape. 

*  Harvey  and  Hird,  Phil.  Mag.  [5],  xxxvi.  p.  45,  1893.     Himstedt,  Wied.  Ann., 
lii.  p.  473,  1894.     J.  J.  Thomson,  Phil.  Mag.  [5],  xl.  p.  511,  1895. 
f  Himstedt,  Wied.  Ann.,  Ixviii.  p.  294,  1899. 
£  Precht,  Wied.  Ann.,  xlix.  p.  50,  1893. 


406 


SPARK   DISCHARGE. 


[212 


Theory  of  the  discharge  from  fine  points. 

212.  We  may  suppose  that  the  escape  of  electricity  from  a  sharp 
point  occurs  in  the  following  way.  When  the  electric  field  at  the 
point  reaches  a  certain  intensity  a  short  spark  passes  from  the 
point  to  the  air  a  little  distance  away,  along  the  path  of  this  spark 
ions  are  produced,  positive  as  well  as  negative ;  if  the  point  is 
positively  electrified  the  positive  ions  are  driven  out  from  this 
region  into  the  surrounding  gas  and  under  the  influence  of  the 
electric  field  find  their  way  to  the  metal  plate  to  which  the  point 
is  discharging;  if  the  point  is  negatively  electrified  it  is  the 
negative  ions  which  are  driven  to  the  plate,  and  which  carry  the 
electricity  which  is  discharging  from  the  point. 

Let  us  apply  these  considerations  to  explain  some  of  the 
features  of  the  discharge.  We  shall  first  consider  the  strength  of 
the  field  required  to  produce  the  small  spark  from  the  point. 

The  relation  between  the  potential  difference  required  to  pro- 
duce a  spark  and  the  spark  length  is  (see  page  360)  represented 
by  a  curve  similar  to  a,  Fig.  116,  where  the  ordinates  represent  the 


Fig.  116. 

spark  potential  and  the  abscissae  the  spark  length.  Let  us  sup- 
pose that  the  point  is  equivalent  in  its  electrical  effect  to  a  small 
sphere  of  radius  a ;  thus  if  V  is  the  potential  of  the  sphere  the 
potential  difference  between  the  sphere  and  a  point  at  a  distance  x 

from  its  surface  is  V  •     — ;   let    the   equation   to   the  curve 


212]  SPARK   DISCHARGE.  407 


a* 


(Fig.  116)  be   y=F-     -,  then   if  the  curve  ft  intersects  the 

Gb  ~F  SO 

curve  a  a  spark  will  pass  from  the  point,  if  the  curves  do  not  intersect 
no  spark  will  pass,  the  smallest  value  of  V  which  will  produce  a 
spark  is  when  the  corresponding  curve  /3  just  touches  the  curve  a. 
Now  when  a  is  very  small  dyfdx  for  0  is  very  small  compared  with 
yjx,  but  for  the  curve  a  it  is  only  in  the  neighbourhood  of  the 
minimum  spark  potential  that  this  is  the  case,  hence  we  conclude 
that  when  {3  touches  a  it  does  so  close  to  A,  the  point  correspond- 
ing to  critical  spark  XQ  and  to  F0  the  minimum  potential  difference 
required  to  produce  a  spark,  hence  we  have  approximately 


F0  here  is  the  value  of  the  minimum  potential  required  to  produce 
a  spark;  we  see  that  V diminishes  as  a  diminishes,  i.e.  the  sharper 
the  point  the  smaller  the  discharge  potential,  it  also  diminishes  as 
the  critical  spark  length  increases,  and  as  the  critical  spark  length 
is  greater  at  low  pressures  than  at  high  the  minimum  potential 
will  diminish  as  the  pressure  diminishes.  In  consequence  of  the 
conductivity  of  the  gas  round  the  point,  the  radius  of  the  sphere 
taken  as  equivalent  in  its  electrical  action  to  the  point  may  be 
considerably  larger  than  the  actual  radius  of  the  point,  and  the 
proportions  between  these  quantities  may  depend  upon  the 
pressure  of  the  gas. 

Difference  between  the  minimum  potential  for  positive 
and  negative  points. 

The  minimum  potential  required  for  the  discharge  of  positive 
electricity  from  a  point  is  greater  than  that  for  negative :  this  is, 
I  think,  consistent  with  the  preceding  view,  for  the  minimum 
potential  difference  F0  depends  (1)  upon  the  energy  a  corpuscle 
must  possess  to  ionise  a  molecule  against  which  it  strikes, 
(2)  upon  the  energy  a  positive  ion  must  possess  in  order  to  make 
the  cathode  against  which  it  strikes  emit  negative  corpuscles; 
an  increase  in  either  of  these  quantities  would  be  attended  by 
an  increase  in  the  minimum  spark  potential.  Now  when  the 


408  SPARK   DISCHARGE.  [212 

discharging  point  is  negatively  electrified  the  conditions  are  the 
same  as  in  the  ordinary  spark  discharge,  for  there  is  a  metallic 
cathode  for  the  positive  ions  to  strike  against  ;  when  however  the 
point  is  positively  electrified,  the  cathode  consists  of  the  molecules 
of  the  gas,  and  it  is  very  probable  that  a  positive  ion  would  require 
greater  energy  to  detach  a  corpuscle  from  a  molecule  of  a  gas  than 
from  a  piece  of  metal  which  we  have  reason  to  think  is  very  easily 
ionised,  this  would  have  the  effect  of  making  F0  for  the  positive 
point  greater  than  for  the  negative  and  thus  making  the  minimum 
potential  required  for  point  discharge  greater. 

Relation  between  the  current  from  a  point  and  the  potential  differ- 
ence between  the  point  and  the  plane  to  which  it  discharges. 

In  order  to  simplify  the  mathematical  analysis  we  shall  take  a 
case  which,  while  presenting  the  same  physical  features  as  the 
point  discharge  from  a  needle,  is  yet  from  its  symmetry  more 
amenable  to  calculation,  the  case  is  that  of  the  discharge  from  a 
very  fine  wire  discharging  to  a  coaxial  cylinder.  Almy*  has  made 
a  series  of  experiments  on  this  kind  of  discharge.  Let  us  take  a 
point  on  the  wire  as  the  origin  for  polar  coordinates  and  let  r  be 
the  distance  of  a  point  in  the  gas  from  the  wire,  R  the  electric 
force  at  this  point  and  p  the  density  of  the  electrification,  then  we 
have 


........................  (1). 

When  we  get  beyond  the  region  of  the  spark  the  discharge  will  be 
carried  by  ions  of  one  sign,  hence  if  i  is  the  current  per  unit  length 
of  the  wire,  u  the  velocity  of  the  ions,  we  have 


but  u  =  kR,  where  k  is  the  velocity  of  the  ion  under  unit  force, 
hence  we  have  from  equation  (1) 

d  /T?  \      2t 

3r(Ai)-B; 

integrating  this  equation,  we  get 

(Rry*  =  jr*  +  C  ........................  (2), 

where  C  is  a  constant.     To  determine  0,  let  a  be  the  smallest 

*  Almy,  American  Journal  of  Science  .[I],  xii.  p.  175,  1902. 


212]  SPARK   DISCHARGE.  409 

value  of  r,  for  which  the  ions  are  all  of  one  sign  (a  will  exceed 
the  radius  of  the  wire  by  a  quantity  of  the  order  of  the  minimum 
spark  length)  ;  when  r  =  a,  R  will  be  comparable  with  the  electric 
force  required  to  produce  a  spark  ;  thus  R  will  at  atmospheric 
pressure  be  greater  than  102  in  electrostatic  units  :  in  these  units 
k  for  air  at  this  pressure  is  450,  hence  unless  i  were  comparable 
with  the  value  2  x  106  in  electrostatic  measure,  i.e.  with  |  x  10~3 
amperes,  which  is  much  larger  than  the  currents  used  by 
observers  of  the  spark  discharge,  (2i/k)  a2  will  be  small  compared 
with  (Rdf,  i.e.  C  will  be  approximately  independent  of  the  current, 

2t 
and  at  the  surface  of  the  wire  C  .will  be  large  compared  with  -y-r2. 

iC 

At  the  surface  of  the  cylinder,  on  fche  other  hand,  in  general,  2ir*/k 
will  be  large  compared  with  C,  for  suppose  the  radius  of  the  cylin- 
der were  103  times  that  of  the  wire,  then  a  current  of  a  few  micro- 
coulombs  per  second  (which  is  of  the  order  of  the  currents  made 
by  Tamm  in  his  experiments)  would  make  2ir2/k  at  the  surface 
of  the  cylinder  very  large  compared  with  (Ra)2  and  therefore  with  C. 

If  V  is  the  potential  at  the  distance  r  from  the  wire,  we  have 
from  (2) 


7  i    T 

dr      r  (k 

integrating  this  equation  we  find,  if  V  is  the  potential  difference 
between  the  cylinder  and  the  point  near  the  wire  where  the  current 
begins  to  be  carried  by  ions  of  one  sign,  and  b  is  the  radius  of  the 
cylinder, 


where   i  is  so  large  that   2tb2/k  is  large  compared  with  C,  this 
becomes  approximately, 


410  SPARK   DISCHARGE.  [212 

the  second  term  on  the  right-hand  side  varies  very  slowly  with  t, 
treating  it  as  a  constant  and  writing  a  for  this  term,  we  get 

&*  =  (F'-a)*    ......................  (1): 


if  V  is  the  potential  difference  between  the  wire  and  the  cylinder 
we  have  seen  that  F=  V  +  F0  where  F0  is  the  least  potential  that 
can  produce  a  spark  (for  air  it  is  about  351  volts),  thus  we  have 
from  (1) 

*  =  ~(F-F0-«y  .....................  (2), 

so  that  for  large  values  of  V,  i  varies  as  F2;  thus  the  current 
varies  as  the  square  of  the  potential  difference.  Almy*  found 
that  the  current  was  proportional  to  V(V—  ft),  thus  for  values  of 
V  large  compared  with  j3  it  is  proportional  to  F2;  according  to 
Almy's  experiments  the  current  is  more  nearly  proportional  to  the 
inverse  cube  of  the  radius  of  the  cylinder  than  to  the  inverse 
square  as  indicated  by  equation  (2)  ;  it  is  to  be  noted  that  any  want 
of  symmetry  in  the  apparatus  which  would  make  the  discharge 
tend  to  concentrate  on  a  particular  radius  would  make  the  current 
vary  more  rapidly  with  the  radius  than  if  the  discharge  were 
quite  symmetrical.  We  see  from  equation  (2)  that  the  current 
varies  as  k,  the  velocity  of  the  ion  under  unit  force,  thus  since  the 
negative  ion  moves  faster  than  the  positive,  the  discharge  under 
given  potential  should  be  greater  when  the  point  is  negative  than 
when  it  is  positive  ;  from  Tamm's  observations  the  ratio  of  the 
negative  current  to  the  positive  in  air  at  atmospheric  pressure  is 
equal  to  1*44,  this  is  not  far  from  the  ratio  of  the  velocities  of  the 
negative  and  positive  ions  for  dry  air. 

Again,  since  i  is  proportional  to  k,  and  k  is  inversely  propor- 
tional to  the  pressure,  the  current  should  vary  inversely  as  the 
pressure  when  the  potential  difference  is  large  ;  a  reference  to  the 
table  on  page  402  will  show  that  although  this  is  approximately 
true  at  high  pressures  it  ceases  to  be  an  approximation  to  the  truth 
when  the  pressure  is  low,  when  the  current  varies  more  nearly  as 
the  inverse  square  of  the  pressure.  At  low  pressures  and  with 
large  currents  the  discharge  is  accompanied  by  luminosity  right 
up  to  the  plate  ;  an  example  of  this  is  shown  in  Fig.  117,  taken 

*  Almy,  American  Journal  of  Science  [4]  xii.  p.  175,  1902. 


212]  SPARK   DISCHARGE.  411 

from  a  paper  by  v.  Obermayer*:  the  appearance  presented  by  the 
discharge  suggests  that  ionisation  is  taking  place  at  the  plate  as 
well  as  at  -the  point,  in  which  case  ions  of  both  signs  would  be 
present  between  the  plate  and  the  point,  and  our  investigation 


Fig.  117. 

which  is  founded  on  the  supposition  that  the  current  is  carried 
entirely  by  ions  of  one  sign  would  not  apply.  Even  at  atmospheric 
pressure  there  is  evidence  in  some  cases  of  the  presence  of  ions 
of  opposite  sign  to  that  of  the  electrification  of  the  discharging 
point :  thus  C.  T.  R.  Wilson -f*  notices  a  case  in  which  when  a 
positive  point  was  discharging  into  his  expansion  apparatus  (see 
p.  136)  an  expansion  which  was  sufficient  to  bring  down  negative 
but  not  positive  ions  produced  a  cloud,  showing  that  negative  ions 
were  present. 

We  shall  see  that  from  a  spark  rays  are  given  out  (Entladung- 
strahlen)  which  can  ionise  a  gas ;  some  rays  are  thus  given  out 
from  the  small  spark  at  the  end  of  the  discharging  point,  and 
these  rays  may  in  certain  cases  produce  appreciable  ionisation 
at  a  considerable  distance  from  the  point.  The  discharge  from  a 
point  seems  to  possess  very  considerable  actinic  power+. 

Earhart's  experiments  (p.  384)  seem  to  indicate  that  when 
the  electric  force  reaches  a  certain  very  high  value  the  ions  can 
come  from  the  metal,  it  would  be  interesting  to  further  test  this 
view  by  seeing  if  a  moderate  potential  was  able  to  produce  a 
discharge  from  an  exceedingly  fine  point  in  a  good  vacuum. 

*  v.  Obermayer,  Wien.  Sitzungsberichte,  c.  p.  127,  1891. 

t  C.  T.  R.  Wilson,  Phil.  Trans.  A.  vol.  cxcii.  p.  403,  1899. 

J  Cook,  Phil.  Mag.  [5],  xlvii.  p.  40, 1899.   Leduc,  Eclair.  Electr.  xxi.  p.  144, 1899. 


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CHAPTER  XIV. 

THE   ELECTRIC   ARC. 

213.  IN  the  electric  spark  and  the  discharge  from  a  point  the 
difference  of  potential  between  the  electrodes  is  several  hundred 
volts,  while  the  current  is  only  a  fraction  of  a  milliampere;  in 
the  case  we  now  proceed  to  consider, — the  electric  arc, — where  the 
electrodes  are  in  a  state  of  incandescence,  the  potential  difference 
is  very  much  smaller,  while  the  current  is  enormously  greater, 
often  amounting  to  many  amperes.  We  can  produce  the  arc 
discharge  if  we  take  a  battery  of  cells  of  small  resistance,  numerous 
enough  to  give  a  potential  difference  of  60  to  80  volts,  and  connect 
the  electrodes  with  two  carbon  terminals  which  are  at  first  pushed 
against  each  other,  a  current  of  electricity  flows  through  the 
carbons  and  warms  the  junction ;  if  while  the  current  is  still 
passing  the  carbons  are  drawn  apart  a  bright  discharge  which 
may  carry  a  current  of  many  amperes  passes  from  one  carbon 
terminal  to  the  other.  This  discharge,  which  is  called  the  electric 
arc,  is  characterized  by  intense  heat  and  light  which  make  it  of 
great  practical  importance.  The  main  sources  of  the  light  are 
the  extremities  of  the  carbon  rods  which  are  in  a  state  of  vivid 
incandescence.  The  temperature  of  the  extremity  of  the  positive 
terminal  is  much  higher  than  that  of  the  negative ;  according  to 
Violle*  the  temperature  of  the  former  is  about  3500°  C.,  that  of 
the  latter  about  2700°  C.,  while  the  temperature  of  the  arc  itself 
he  found  to  be  higher  than  that  of  either  terminal.  The  terminals 
if  similar  to  begin  with  soon  present  marked  differences  in  their 
appearance,  the  extremity  of  the  positive  terminal  gets  hollowed 
out  into  a  crater-like  shape,  while  the  negative  terminal  if  pointed 
to  begin  with  remains  so.  Both  terminals  in  general  lose  weight, 

*  Violle,  Comptes  Rendus,  cxv.  p.  1273,  1892. 


214] 


THE   ELECTRIC   ARC. 


417 


the  positive,  however,  far  more  than  the  negative.  The  appearance 
of  the  terminals  is  shown  in  Fig.  118;  these  figures  are  due  to 
Mrs  Ayrton  *.  a  and  b  represent  the  appearance  when  the  arc  is 
quiet,  d  when  it  is  giving  out  a  hissing  sound ;  in  some  cases  a 
mushroom-shaped  body  forms  at  the  end  of  the  negative  terminal. 


Fig.  118. 

The  temperature  of  the  crater  of  the  positive  terminal  remains 
constant  even  when  the  current  varies,  an  increase  of  current 
increases  the  area  of  the  luminous  crater,  but  the  amount  of 
light  given  out  by  each  unit  area  remains  unaltered  ;  the  tem- 
perature of  the  crater  is  probably  the  temperature  at  which 
carbon  melts  or  volatilizes.  E.  W.  Wilson  f  has  shown  that  when 
the  arc  passes  through  gas  at  a  very  high  pressure,  say  20  atmo- 
spheres, the  luminosity  of  the  positive  crater  is  sensibly  less  than 
at  atmospheric  pressure  ;  in  a  later  paper  he  gives  reasons  for 
thinking  that  this  may  be  explained  by  the  increased  absorption 
of  light  by  the  gas  surrounding  the  arc. 


Connection  between  the  difference  of  potential  between  the 
electrodes,  the  length  of  the  arc,  and  the  current. 

214.     If  V  is  the  potential  difference  between  the  terminals, 
I  the  length  of  the  arc,  FrohlichJ  showed  that  the  linear  relation 


where  ra  and  n  are  constants,  i.e.  independent  of  I,  exists  between 

*  Mrs  Ayrton,  Proc.  Inst.  Electrical  Engineers,  xxviii.  p.  400,  1899. 
t  E.  W.  Wilson,  Proc.  Roy.  Soc.,  Iviii.  p.  174,  1895  ;  Ix.  p.  377,  1897. 
£  Frohlich,  Elektrotechnische  Zeitschrift,  iv.  p.  150,  1883. 


T.  G. 


27 


418 


THE   ELECTRIC   ARC. 


[214 


V  and  I.    Mrs  Ayrton*  has  shown  that  both  m  and  n  are  functions 
of  the  current  i  passing  through  the  arc,  and  that 


where  a,  /3,  7,  8  are  constants. 

Ayrton-f-  made  a  long  series  of  experiments  on  the  relation 
between  the  potential  difference  and  the  current  through  the  arc, 
some  of  the  curves  representing  the  results  of  these  experiments 
are  given  in  Fig.  -119,  where  the  ordinates  represent  the  potential 


a      20     22       24      26      28     30  Amperes 


difference  and  the  abscissae  the  current;  it  will  be  seen  from 
these  curves  that  for  a  quiet  arc  an  increase  in  current  is  accom- 
panied by  a  decrease  in  the  potential  difference,  while  in  the 
hissing  arc  the  potential  difference  is  independent  of  the  current. 

The  constants  m  and  n  in  Frohlich's  formula  have  been 
measured  by  several  experimenters,  by  Frohlich  himself,  EdlundJ, 
Peukert§,  v.  Lang||,  Gross  and  ShephardU,  Nebel**,  Aronsff, 

*  Mrs  Ayrton,  The  Electric  Arc,  chap.  iv. 

f  W.  E.  Ayrton.     Mrs  Ayrton,  The  Electric  Arc. 

J  Edlund,  Fogg.  Ann.,  134,  pp.  251,  337,  1868. 

§  Peukert,  Zeitschrift  fur  Elektrotechnik,  Wien,  iii.  p.  Ill,  1885. 

||  v.  Lang,  Wied.  Ann.,  xxvi.  p.  145,  1885 ;  xxxi.  p.  384,  1887. 

IT  Gross  and  Shephard,  Proc.  Amer.  Acad.  of  Sciences,  1886,  p.  2. 

**  Nebel,  Centralblatt  fiir  Elektrotechnik,  viii.  pp.  517,  619,  1886. 

ft  Arons,  Wied.  Ann.,  Iviii.  p.  73,  1896. 


214]  THE   ELECTRIC   ARC.  419 

Luggin*;  for  carbon  electrodes  in  air  at  atmospheric  pressure  m 
is  about  39  volts,  varying  somewhat  with  the  size  and  purity  of 
the  carbons;  it  is  diminished  by  soaking  these  in  salt  solution; 
the  value  of  n  given  by  different  experimeters  varies  considerably, 
this  may  be  due  to  their  haviog  used  currents  of  different  inten- 
sities, as  Mrs  Ayrton  has  shown  that  it  depends  upon  the  current, 
diminishing  as  the  current  increases.  When  metallic  instead  of 
carbon  terminals  are  used  the  value  of  m  depends  upon  the  metal 
being  in  general  larger  the  higher  the  temperature  at  which  the 
metal  volatilizes;  the  values  in  volts  found  by  v.  Langf  for  m  for 
terminals  of  different  substances  are  as  follows  :  C  =  35,  Pt  =  27 '4, 
Fe  =  25,  Ni=  26-18,  Cu  =  23'86,  Ag=15'23,  Zn  =  19*86,  Cd  =  10'28. 
Lecher J  gives  Pt  =  28,  Fe  =  20,  Ag  =  8.  Arons§  found  for  Hg  the 
value  12*8,  in  this  case  the  fall  of  potential  along  the  arc  itself 
was  abnormally  small.  In  interpreting  these  results  it  is  important 
to  notice  that  with  some  terminals  the  arc  is  intermittent. 
Lecher  has  shown  that  this  is  the  case  with  iron  or  platinum 
terminals,  and  Arons  that  it  is  so  with  mercury  terminals;  no 
intermittence  has  been  detected  with  carbon,  silver  or  copper 
terminals.  The  potential  differences  given  above  are  mean  values, 
and  if  the  arc  is  intermittent  they  may  differ  greatly  from  the 
actual  potentials  during  the  passage  of  the  arc. 

If  the  two  terminals  are  of  different  materials  the  potential 
difference  may  depend  upon  the  direction  of  the  currents,  this 
is  especially  the  case  when  one  of  the  electrodes  is  carbon  and  the 
other  metal ;  the  arc  passes  much  more  easily  when  the  carbon  is 
the  negative  terminal  and  the  metal  the  positive  one  than  it  does 
in  the  opposite  direction.  So  marked  is  this  effect  that  if  such 
a  pair  of  terminals  is  connected  up  with  an  alternating  electro- 
motive force  the  arc  may  pass  only  in  the  direction  in  which  the 
carbon  is  the  negative  terminal,  the  potential  difference  being 
insufficient  to  drive  it  the  opposite  way.  For  experiments  on  this 
point  we  may  refer  to  papers  by  Blondel||,  by  Duddell  and 
MarchantH,  and  by  Eichberg  and  Kallir**. 

*  Luggin,  Wien.  Ber.,  xcviii.  p.  1192,  1889. 

t  v.  Lang,  Wied.  Ann.,  xxxi.  p.  384,  1887. 

$  Lecher,  Wied.  Ann.,  xxxiii.  p.  609,  1888. 

§  Arons,  Wied.  Ann.  Iviii.  p.  73,  1896. 

||  Blondel,  Comptes  Bendus,  127,  p.  1016,  1898;  128,  p.  727,  1898. 

IT  Duddell  and  Maxchant,  Inst.  Elect.  Eng.,  xxviii.  p.  1,  1899. 

**  Eichberg  and  Kallir,  Wien.  Sitz.  107,  p.  657,  1898. 

27—2 


420 


THE   ELECTRIC   ARC. 


[215 


Non-arcing  Metals. 

215.  With  some  metals  as   terminals  the   arc    has   a  great 
tendency  to  go  out  and  is  only  maintained  with  difficulty;   brass, 
cadmium,  and  bismuth  are  examples  of  such  metals ;  in  some  cases 
this  is  a  very  useful  property,  it  has  been  investigated  by  Wurtz*  : 
a  great  deal  depends  upon  the  size  and  shape  of  the  electrodes,  as 
well  as  of  the  material  they  are  made ;  conditions  which  promote 
a  rapid  flow  of  heat  from  the  hot  extremities  of  the  terminals  are 
favourable  to  the  extinction  of  the  arc. 

Effect  of  pressure  on  the  potential  difference  in  the 
arc  discharge. 

216.  The  potential  difference  is  not  independent  of  the  pres- 
sure of  the  gas  through  which  the  arc  passes.     Duncan,  Rowland 
and  Todd  •(•  have  made  an  extensive  series  of  experiments  on  this 
point ;  the  results  of  some  of  their  experiments  are  represented 
graphically  in  Fig.  120:  it  will  be  seen  from  the  curves  that  for 

80 


70 


60 


50 


40 


30 


Aimosphe 


es 


Fig.  120. 


short  arcs  the  potential  difference  increases  continuously  with  the 
pressure,  while  for  longer  arcs  there  is  a  critical  pressure  at  which 
the  potential  difference  is  a  minimum ;  this  critical  pressure  seems 
to  increase  with  the  length  of  the  arc. 

*  Wurtz,  Lum.  EL,  xlv.  p.  79,  1892. 

f  Duncan,  Rowland  and  Todd,  Electrician,  xxxi.  p.  60. 


217] 


THE   ELECTRIC   ARC. 


421 


Effect  of  the  nature  of  the  gas  on  the  potential  difference. 

217.  The  nature  of  the  gas  affects  the  arc,  thus  it  is  difficult 
to  get  good  arcs  in  pure  hydrogen  ;  this  may  be  due  in  part  at  least 
to  the  more  rapid  convection  of  heat  from  the  terminals  in  this  gas. 
Arons*  has  measured  the  potential  difference  required  to  produce 
an  arc  1*5  mm.  long,  carrying  a  current  of  4*5  amperes  between 
terminals  of  different  metals  in  air  and  pure  nitrogen ;  his  results 
are  given  in  the  following  table : 


Potential 

difference 

Potential 

difference 

Terminal 

Air 

Nitrogen 

Terminal 

Air 

Nitrogen 

Ag 

21 

? 

Pt    

36 

30 

Zn!; 

23 

21 

Al       

39 

27 

Cd  

25 

21 

Pb    

18 

Cu  

27 

30 

Mg  .. 

22 

Fe  

29 

20 

The  case  of  silver  is  interesting  as,  though  it  gives  good  arcs 
in  air,  Arons  could  not  obtain  an  arc  in  pure  nitrogen  ;  he  ascribes 
this  to  the  absence  of  any  chemical  combination  between  the 
silver  and  the  nitrogen ;  he  was  able  in  the  case  of  the  other 
metals  to  get  evidence  of  the  formation  of  nitrides.  With  the 
exception  of  copper  the  potential  differences  in  nitrogen  are  smaller 
than  in  air,  the  difference  being  very  noticeable  in  the  cases  of 
iron  and  aluminium. 

Arons  also  made  a  series  of  experiments  in  hydrogen,  but 
found  the  greatest  difficulty  in  producing  the  arc  in  this  gas,  and 
could  only  obtain  it  by  using  large  currents  and  having  the  gas  at 
a  low  pressure ;  cadmium,  zinc,  and  magnesium  gave  the  best  arcs 
in  hydrogen. 

We  must  in  the  case  of  the  arc  remember  that  since  the  metal 
or  the  carbon  volatilizes  the  arc  goes  through  a  mixture  of  the 
vapour  of  the  metal  and  the  air,  nitrogen  or  hydrogen  in  which 
the  terminals  are  immersed,  so  that  the  conditions  of  the  experi- 
ment are  very  complicated ;  the  presence  of  this  vapour  makes 

*  Arons,  Drude's  Annalen,  i.  p.  700,  1900. 


422  THE   ELECTRIC   ARC.  [218 

ambiguous  the  interpretation  of  the  effect  of  changes  of  pressure 
in  the  gas  around  the  terminals,  as  we  do  not  know  the  pressure  of 
this  vapour. 

218.  The  distribution  of  potential  between  the  terminals 
generally  shows  the  following  characteristics :  there  is  a  consider- 
able fall  of  potential  close  to  the  anode,  a  smaller  one  close  to  the 
cathode,  and  a  very  gentle  potential  gradient  in  the  space  between 
the  terminals ;  the  general  nature  of  this  distribution  is  shown  by 
the  curve  in  Fig.  121:  the  curve  shows  many  of  the  characteristics 


CATHODE  ANODE 

Fig.  121. 

of  the  distribution  of  potential  between  two  hot  electrodes  in 
flames;  see  p.  191. 

Luggin*  found  that  with  carbon  terminals  and  a  current  of 
15  amperes  there  was  a  fall  of  potential  of  33'7  volts  close  to  the 
anode,  and  one  of  87  close  to  the  cathode.  The  difference  between 
the  potential  falls  at  the  anode  and  cathode  is  not  so  large  with 
iron  or  copper  electrodes  as  it  is  with  carbon.  With  mercury 
terminals  Arons  found  that  the  cathode  fall  was  5 '4  volts,  the 
anode  fall  7'4  volts.  When  the  current  is  increased  so  much 
that  the  discharge  passes  from  the  quiet  to  the  hissing  arc  there 
is  a  sudden  fall  of  potential.  Luggin f  and  Mrs  AyrtonJ  have 
shown  that  this  diminution  in  the  potential  occurs  almost  entirely 
at  the  anode,  the  potential  gradients  in  the  other  parts  of  the 
discharge  being  but  little  atfected. 

*  Luggin,  Centralblatt  filr  Elektrotechnik,  x.  p.  567,  1888. 
t  Luggin,  Wien.  Sitz.,  xcviii.  p.  1192,  1889. 
J  Mrs  Ayrton,  The  Electric  Arc. 


219]  THE   ELECTRIC   ARC.  423 

219.  Some  experiments  which  are  very  suggestive  as  to  the 
parts  played  by  the  two  terminals  in  the  arc  discharge  have  been 
made  by  Fleming*.  In  these  experiments  a  third  exploring  carbon 
electrode  was  used  which  was  either  inserted  in  the  arc,  or  what  was 
often  more  convenient,  placed  outside  the  undisturbed  path  of 
the  arc,  and  the  arc  directed  on  to  it  by  means  of  a  magnet. 
Fleming  found  that  when  the  third  terminal  was  connected 
with  the  negative  terminal  of  the  arc  by  a  circuit  which  con- 
tained a  battery  of  a  few  cells  and  a  galvanometer  to  register  the 
current,  a  current  passed  round  the  circuit  under  a  very  small 
electromotive  force  when  the  direction  of  the  current  was  from 
the  cold  electrode  placed  in  the  arc  through  the  arc  to  its  negative 
terminal  and  then  through  the  galvanometer,  but  that  it  would 
not  pass  in  the  other  direction  :  another  way  of  stating  this  result 
is  to  say  that  with  one  electrode  hot  and  the  other  cold,  a  current 
can  pass  in  the  direction  in  which  the  negative  electricity  comes 
from  the  hot  electrode  into  the  gas,  but  not  in  the  other  direction. 
Thus  although  in  ordinary  arcs  the  positive  terminal  is  the  hotter, 
this  experiment  shows  that  a  high  temperature  of  the  negative 
electrode  is  the  essential  condition  for  the  arc  discharge,  and  that 
if  we  can  keep  the  temperature  of  the  negative  terminal  up  by 
independent  means  we  can  get  a  discharge,  even  although  the 
temperature  of  the  positive  electrode  is  comparatively  low.  No 
arc,  however,  will  pass  if  the  negative  terminal  is  cold. 

Fleming  found  that  if  he  connected  the  exploring  electrode 
up  to  the  positive  electrode,  without  introducing  any  battery  into 
the  circuit,  enough  current  passed  through  the  exploring  electrode 
to  ring  an  electric  bell  or  light  an  incandescent  lamp  placed 
between  the  electrode  and  the  positive  terminal :  but  that  no 
appreciable  current  passed  if  the  electrode  were  connected  with 
the  negative  instead  of  the  positive  terminal ;  this  result  indicates 
that  the  potential  of  the  spare  electrode  is  brought  nearly  to  an 
equality  with  that  of  the  cathode.  From  these  experiments 
Fleming  concluded  that  the  arc  discharge  consists  of  a  torrent 
of  negatively  electrified  particles  of  carbon  shot  off  from  the 
cathode,  these  carry  the  current  and  striking  with  great  violence 
against  the  anode  hollow  it  out,  just  as  a  body  is  hollowed  out  ' 
when  struck  by  a  sand  blast. 

*  Fleming,  Proc.  Roy.  Soc.,  xlvii.  p.  123,  1890. 


424  THE   ELECTRIC   ARC.  [219 

The  phenomena  connected  with  the  discharge  of  electricity 
from  incandescent  bodies  (see  Chap.  VIII.)  seem  to  me  to  indicate 
a  somewhat  different  explanation  of  the  arc  discharge.  We  saw 
that  an  incandescent  body  such  as  a  piece  of  carbon,  even  when 
at  a  temperature  far  below  that  of  the  terminals  in  the  arc 
discharge,  emits  negatively  electrified  corpuscles  at  a  rate  corre- 
sponding to  a  current  of  the  order  of  an  ampere  per  square 
centimetre  of  incandescent  surface,  and  that  the  rate  of  emission 
increases  very  rapidly  with  the  temperature ;  thus  at  the  tem- 
perature of  the  negative  carbon  in  the  arc  the  rate  of  emission 
probably  corresponds  to  a  current  of  a  large  number  of  amperes 
per  square  centimetre  of  hot  surface.  If  then  a  piece  of  carbon 
were  maintained  by  independent  means  at  this  high  temperature 
and  if  this  were  used  as  the  negative  electrode  a  current  could 
be  sent  through  a  gas  to  another  electrode,  whether  this  second 
electrode  were  cold  or  hot. 

Let  us  first  suppose  that  the  anode  is  cold,  then  the  current  would 
be  carried  entirely  by  negative  ions,  there  would .  be  free  negative 
ions  in  the  space  between  the  electrodes,  these  would  cause  the 
electric  force  to  increase  as  we  pass  from  the  cathode  to  the  anode 
and  would  make  the  current  increase  rapidly  with  the  potential 
difference.  Now  suppose  that  the  anode  becomes  hot  and  that 
there  is  some  gas  in  contact  with  it  which  can  be  ionised,  yield- 
ing a  supply  of  positive  ions ;  this  current  will  no  longer  be 
carried  entirely  by  negative  ions,  though  inasmuch  as  (p.  192) 
the  velocity  of  the  negative  ion  at  these  high  temperatures  is 
very  much  greater  than  that  of  the  positive,  by  far  the  larger  part 
of  the  current  is  carried  by  the  negative  ions.  The  presence  of 
the  positive  ions,  however,  modifies  very  considerably  the  distri- 
bution of  potential  between  the  electrodes :  the  positive  ions 
diffuse  into  the  region  of  the  discharge  until  they  are  sensibly 
equal  in  number  to  the  negative  ions ;  when  this  is  the  case  the 
electric  force  is  sensibly  uniform  between  the  terminals  except  close 
to  the  electrodes,  and  we  have  a  distribution  similar  to  that  given 
in  Fig.  49,  p.  191,  which  is  taken  from  a  paper  by  H.  A.  Wilson  on  the 
conductivity  through  hot  gases,  and  represents  the  distribution  of 
potential  between  two  hot  electrodes :  by  comparison  with  Fig.  121 
it  will  be  seen  that  this  bears  a  great  resemblance  to  the  distri- 
bution of  potential  between  the  terminals  in  the  arc  discharge. 


220]  THE   ELECTRIC   ARC.  425 

The  view  we  take  of  the  arc  discharge  is  that  it  is  similar  to  the 
discharge  between  the  incandescent  terminals  just  considered,  the 
only  difference  being  that  in  the  flame  the  temperature  of  the 
terminals  is  maintained  by  independent  means,  while  in  the  arc  it  is 
maintained  by  the  work  done  by  the  discharge  itself;  this  requires 
that  the  potential  difference  between  the  electrodes  also  and  the 
current  passing  between  them  should  not  sink  below  certain  values. 
On  the  other  hand  when  the  temperature  is  maintained  by  external 
aid  the  smallest  potential  difference  is  able  to  send  a  current. 

On  this  view  the  cathode  is  bombarded  by  the  positive  ions 
which  maintains  its  temperature  at  such  a  high  value  that  negative 
corpuscles  come  out  of  the  cathode ;  these  which  carry  by  far  the 
larger  part  of  the  arc  discharge  bombard  the  anode  and  keep  it 
at  incandescence,  they  ionise  also  either  directly  by  collision  or 
indirectly  by  heating  the  anode,  the  gas  or  vapour  of  the  metal  of 
which  the  anode  is  made  producing  in  this  way  the  supply  of 
positive  ions  which  keep  the  cathode  hot.  It  will  be  seen  that 
the  essential  feature  in  the  discharge  is  the  hot  cathode,  as  this 
has  to  supply  the  carriers  of  the  greater  part  of  the  current  in  the 
arc ;  the  anode  has  in  general  to  be  hot,  otherwise  it  could  not 
supply  the  positive  ions  which  keep  the  cathode  hot ;  in  such  a 
case  as  that  of  a  third  electrode  put  in  the  arc  and  acting  as 
one  of  the  anodes  we  may  regard  the  discharge  as  having  two 
anodes,  and  as  one  is  sufficient  to  keep  the  cathode  hot  we 
can  get  the  arc  to  pass  to  the  other  anode  even  although  it 
is  cold. 

220.  The  conditions  that  determine  the  current  when  a 
given  electromotive  force  acts  round  the  whole  circuit  of  the 
arc  are  that  the  work  supplied  to  the  cathode  and  anode  should 
be  sufficient  to  maintain  them  at  incandescence.  Although  we 
have  not  the  data  which  would  make  a  numerical  calculation 
possible,  yet  an  expression  in  an  analytical  form  of  these  con- 
ditions may  serve  to  make  the  preceding  theory  clearer  and  more 
definite. 

We  have  seen  that  the  number  of  corpuscles  emitted  in  one 
second  by  unit  area  of  a  hot  body  increases  very  rapidly  with  the 

temperature,    being   represented  with   considerable   accuracy  by 

_«> 
a  formula  of  the  form  AO^e   *,  where  6  is  the  absolute  temperature; 


426  THE   ELECTRIC   ARC.  [220 

we  shall  call  this  function  /(#),  then  if  6  is  the  temperature  and 
wl  the  area  of  the  luminous  part  of  the  cathode  the  number  of 
corpuscles  coming  from  the  cathode  in  one  second  is  equal  to 
w-if(6).  If  i  is  the  current,  R1}  R^  the  velocities  of  the  positive 
and  negative  ions  under  unit  electric  force,  the  part  of  the 
current  carried  by  the  negative  ions  is  R.2i/(Rl  +  R2),  and  this 
when  divided  by  e,  the  charge  on  an  ion,  is  equal  to  the  number 
of  negative  ions  passing  a  section  of  the  arc  per  second  ;  hence 
we  have 


Let  us  now  consider  the  temperature  equilibrium  of  the 
cathode.  Let  w^  (0)  be  the  rate  at  which  it  is  losing  heat  by 
radiation  and  conduction,  w  the  work  expended  when  the  cathode 
emits  one  corpuscle,  then  to  maintain  thermal  equilibrium  the 
rate  at  which  energy  must  be  given  to  the  cathode  is 

w      ^2       • 


this  work  has  to  be  supplied  by  the  positive  ions  coming  up  to 
the  cathode  in  unit  time  ;  the  number  of  such  ions  is 


we  shall  suppose  that  the  energy  they  possess  is  got  in  passing 
through  the  fall  of  potential  at  the  cathode;  let  this  fall  be 
denoted  by  E0,  then  equating  the  rate  at  which  energy  is  com- 
municated to  the  cathode  to  the  rate  at  which  the  cathode  is 
losing  energy  we  get 


or 


I 

Let  6l  be  the  temperature  and  o>2  the  area  of  the  hot  part  of 
the  anode,  w^r  (6^  the  rate  at  which  it  is  losing  energy  by 
radiation,  conduction,  and  vaporisation,  W  the  amount  of  work 
required  to  produce  a  positive  ion. 

The  number  of  positive  ions  produced  in  unit  time  is 

R!        £ 

RI  +  R2  e  ' 


220]  THE   ELECTRIC   ARC.  427 

thus  the  work  absorbed  per  second  at  the  cathode  is 

Ri       Wi 


The  number  of  negative  ions  striking  against  the  anode  in 
unit  time  is 


let  us  suppose  that  the  energy  with  which  they  strike  against 
the  anode  is  that  due  to  passing  through  the  anode  fall  of 
potential  Elf  equating  the  rate  at  which  the  anode  is  losing 
energy  to  that  at  which  it  is  gaining  it  we  have 


thus 


#!  ,  as  we  have  seen,  does  not  depend  on  the  current  but  only  on  the 
material  of  which  the  anode  is  made. 

If  E  is  the  external  electromotive  force  acting  on  the  circuit, 
R  the  resistance  of  the  leads,  then  E—  Ri  is  the  potential 
difference  between  the  arc  terminals  ;  when  the  arc  is  so  short 
that  we  may  neglect  the  changes  in  potential  along  the  arc,  apart 
from  those  at  the  anode  and  cathode,  this  difference  of  potential 
is  equal  to  E0  -f  El  ;  hence  we  have 

E-Ri=E«  +  E,  ........................  (4); 

thus  we  have  four  equations  (1),  (2),  (3),  and  (4)  to  determine  the 
four  quantities  6,  i,  E0,  and  Elf 

Mrs  Ayrton  has  shown  that  o>2  the  area  of  the  crater  is  a  linear 
function  of  the  current  and  may  be  represented  by  an  equation  of 
the  form  o>2  =  a  +  bi  ;  if  o>!  follows  the  same  law  then  equations  (2) 

ft 

and  (3)  suggest  that  E0  +  E^  will  be  of  the  form  a  +  —  ,  where 

a  and  ft  are  independent  of  i,  and  this  is  in  accordance  with  the 
results  of  the  experiments  made  on  the  relation  between  the 
current  through  the  arc  and  the  potential  difference  between  its 
terminals. 


428 


THE   ELECTRIC   ARC. 


[221 


221. 


Taking  the  equation 
E 


.(5), 


we  see  that  the  graph  representing  this  relation  is  a  hyperbola. 
E  has  a  minimum  value  at  the  point  A,  this  value  is 

2  V^K  +  a. 

The  portion  of  the  graph  to  the  left  of  A  corresponds  to  an  unstable 
state,  for  suppose  the  current  is  changed  from  iQ  to  i0  +  x  and 


Fig.  122. 

that  there  is  self-induction  L  in  the  external  circuit,  let  E'  be  the 
steady  electromotive  force  due  to  batteries,  &c.,  in  this  circuit, 
then  from  (5)  we  have 


or  when  x  is  small 


or 


dx 


/3 


Now  to  the  left  of  A,  ~  —  R  is  positive,  hence  x  will  increase 

indefinitely  with  t  and  the  current  will  be  unstable ;  to  the  right 
of  A  this  quantity  is  negative  and  x  will  diminish  to  zero  as  the 
time  increases,  the  current  under  these  conditions  will  be  stable. 
Thus  for  stability  the  current  cannot  be  less  than  its  value  at  A, 
i.e.  (ft/R)*,  hence  if  im  is  the  minimum  current,  Em  the  minimum 
external  electromotive  force,  we  have 

4,=  (/SAB)*, 


222]  THE    ELECTRIC   ARC.  429 

or  if  the  external  electromotive  force  is  E  the  arc  will  go  out  if 
the  resistance  R  in  the  external  circuit  is  greater  than 

(E-af 
~4£ 

Thus  as  one  numerical  example  let  us  take  the  case  of  the 
arc  6  mm.  in  length  for  which  the  curve  representing  the  relation 
between  the  current  through  the  arc  and  the  potential  difference 
between  the  terminals  is  represented  in  Fig.  119,  page  418;  from 
the  curve  we  find  that  /3  =  3'4  x  108  in  absolute  measure ;  we  may 
take  a  as  about  40  volts,  or  in  absolute  measure  4  x  109  if  E  the 
electromotive  force  in  the  external  circuit  is  80  volts  or  8  x  109 
absolute  units ;  we  find  that  the  arc  will  go  out  if  the  resistance 
is  greater  than 

16  x  1018 


4x3'4xl08 


l-2xl010=12ohms. 


222.    Another  way  of  treating  the  problem  of  the  arc  graphically 
is,  instead  of  tracing  the  curve 


where  F(i)  is  the  potential  difference  between  the  terminals  of  the 
arc  when  it  is  carrying  the  current  i,  to  trace  the  curve 

y=F(i) 

and  the  straight  line 

y^E-Ri', 

if  these  intersect  in  two  points  P  and  Q  (Fig.  123)  we  can  show  as 
before  that  the  state  corresponding  to  P  is  unstable,  and  that  the 
current  under  the  given  external  electromotive  force  and  resistance 
is  represented  by  the  abscissa  of  the  point  Q  ;  if  the  resistance  is  too 
great  the  line  may  not  cut  the  curve  at  all,  while  if  it  is  too  small 
the  point  Q  may  be  so  far  away  that  the  corresponding  value  of 
the  current  may  be  too  great  for  a  silent  arc  and  a  hissing  arc  will 
necessarily  be  formed. 

The  minimum  current  for  a  given  external  resistance  is  got 
by  finding  the  point  8  when  the  tangent  to  the  curve  is  parallel 
to  the  line  y  —  —  Ri.  The  current  at  8  is  the  minimum  current, 
and  the  value  of  OT,  T  being  the  point  where  the  tangent  at  8 
intercepts  the  axis  i  =  0,  is  the  minimum  external  electromotive 
force. 


430 


THE   ELECTRIC   ARC. 


[223 


To  find  the  maximum  value  of  R  for  which  the  arc  can  exist 
under  a  given  external  electromotive  force,  EI  take  ON=Ely  and 
from  N  draw  a  tangent  to  the  curve;  let  this  tangent  cut  the 
axis  y  =  0  in  M,  then  ON/OM  is  the  required  resistance. 

223.  Hissing  Arcs.  When  the  current  is  increased  beyond 
a  certain  value,  the  potential  difference  between  the  terminals 
falls  in  the  case  of  carbon  electrodes  by  about  8  or  10  volts  and 
does  not  change  when  the  current  is  increased ;  when  in  this  state, 
the  arc  emits  a  hissing  sound.  Mrs  Ayrton*,  who  has  made  a 
study  of  the  hissing  arc,  has  shown  that  it  occurs  when  the 
incandescence  of  the  anode  covers  such  a  large  area  that  it 
expands  beyond  the  crater  up  the  sides  of  the  terminal :  see 
Figs.  118,  c  and  a,  which  represent  the  appearance  of  the  arc  in 


CURRENT 
Fig.  123. 

the  hissing  and  quiet  stages.  The  hissing  of  the  arc  is  closely 
connected  with  the  oxidation  of  the  terminal  by  the  air ;  for  when 
the  incandescence  extends  up  the  sides  of  the  carbon,  the  glowing 
carbon  is  no  longer  completely  protected  by  the  carbon  vapour 

*  Mrs  Ayrton,  The  Electric  Arc. 


224]  THE   ELECTRIC  ARC.  431 

from  oxidation.  It  is  then  that  the  arc  hisses.  Mrs  Ayrton  has 
shown  that  if  the  arc  is  formed  in  a  closed  vessel  an  increase  of 
current  ceases  to  make  it  hiss  as  soon  as  the  oxygen  in  the  vessel 
has  been  burnt  up;  whenever,  however,  fresh  oxygen  is  intro- 
duced into  the  vessel  the  hissing  recommences. 

We  can  see  why  chemical  combination  should  tend  to  diminish 
the  potential  difference  between  the  terminals  of  the  arc,  for  the 
heat  evolved  by  the  burning  of  the  terminals  would  tend  to 
maintain  them  at  incandescence,  so  that  the  whole  of  the  energy 
required  for  this  purpose  would  no  longer  have  to  be  supplied  by 
the  electric  field. 

Trotter*  has  shown  that  parts  of  the  arc  are  in  rapid  motion 
in  the  unstable  state  between  the  hissing  and  the  quiet  arc. 

224.  Effect  of  a  magnetic  field  on  the  arc.  The  arc  is 
deflected  by  a  magnetic  field  in  the  same  direction  as  a  flexible 
conductor  would  be  if  it  carried  a  current  flowing  in  the  same 
direction  as  that  through  the  arc.  The  curved  course  corresponds 
to  a  longer  path  and  the  effect  of  the  magnetic  field  on  the 
potential  difference  is  of  the  same  character  as  an  increase  in  the 
length  of  the  arc,  and  just  as  it  is  possible  to  extinguish  an  arc 
by  increasing  its  length,  so  the  arc  can  be  blown  out  by  the 
application  of  a  strong  magnetic  field. 

*  Trotter,  Proc.  Roy.  Soc.  Ivi.  p.  262,  1894. 


V 


CHAPTER  XV. 

DISCHARGE   THROUGH   GASES  AT   LOW  PRESSURES. 

225.  WHEN  the  electric  discharge  passes  through  a  gas  at 
a  low  pressure  differences  in  the  appearance  of  the  discharge  at 
various  points  in  its  path  become  very  clearly  marked.  The 
discharge  (Fig.  124)  presents  the  following  features :  starting  from 
the  cathode  there  is  a  thin  layer  of  luminosity  spread  over  its 


Fig.  124. 

surface,  next  to  this  there  is  a  comparativelyjdark  space,  called 
the  Crookes  dark  space,  the  width  of  which  depends  on  the 
pressure  of  the  gas,  increasing  as  the  pressure  diminishes,  it  also 


225]         DISCHARGE  THROUGH   GASES  AT  LOW   PRESSURES.  433 

* 
as  Schuster*  has  shown  depends  to  some  extent  on  the  intensity 

of  the  current,  being  greater  for  large  currents  than  for  small ; 
the  boundary  of  the  dark  space  is  approximately  the  surface 
traced  out  by  normals  of  constant  length  drawn  to  the  surface 
of  the  cathode;  beyond  the  dark  space  there  is  a  luminous  region 
called  the  'negative  glow';  beyond  this  again  is  another  com- 
paratively dark  region  called  by  some  writers  the  'second  negative 
dark  space/  and  by  others  the  '  Faraday  dark  space/  its  length  is 
very  variable  even  when  the  pressure  is  constant ;  beyond  this; 
again  there  is  a  luminous  column  reaching  right  up  to  the  anode 
and  called  the  'positive  column';  when  the  current  and  pressure 
are  within  certain  limits  this  column  exhibits  remarkable  alter- 
nations of  dark  and  bright  spaces,  these  are  called  striations  and 
are  shown  in  Fig.  125.  The  figure  is  taken  from  a  paper  by 


mm :m*mmm  mm  m  m  mm   r? 
~i*«ii*ttt*ifiiiif  itiiii         t*..  • 

Mill!!  •** 


Fig.  125. 

De  la  Rue  and  Mtiller,  Phil.  Trans.,  1878,  pt.  1,  p.  155.     In  long 
tubes  the  positive  column  constitutes  by  far  the  greater  part  of 

*  Schuster,  Proc.  Eoy.  Soc.  xlvii.  p.  557,  1890. 
T.  G.  28 


434  DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.         [226 

the  discharge,  for  the  Crookes  space,  the  negative  glow,  and  the 
Faraday  dark  space -do  not  depend  markedly  upon  the  length  of 
the  tube,  so  that  when  the  length  of  the  discharge  is  increased, 
the  increase  is  practically  only  in  the  length  of  the  positive 
column;  thus  for  example  in  a  tube  used  by  the  writer  about 
15  metres  long  the  positive  column  occupied  the  whole  of  the 
tube  with  the  exception  of  two  or  three  centimetres  close  to 
the  cathode. 

Distribution  of  the  Electric  Force  along  the  discharge. 

226.  The  electric  force  varies  greatly  along  the  discharge,  it 
has  been  measured  by  Hittorf*,  Graham -f-,  A.  Here},  Skinner §, 
and  H.  A.  Wilson  ||.  The  method  employed  by  these  observers 
was  to  measure  the  potential  acquired  by  a  metal  wire  placed  in 
various  positions  along  the  line  of  discharge,  if  the  potential  of 
the  wire  is  the  same  as  that  of  the  gas  with  which  it  is  in  contact 
we  get  from  these  observations  the  means  of  determining  the  dis- 
tribution of  electric  force  along  the  tube.  As  an  example  of  how 
this  method  is  carried  out  in  practice  we  may  take  the  apparatus 
used  by  H.  A.  Wilson  and  shown  in  Fig.  126.  The  discharge 


—  To  fi/Atp  ere 


Fig.  126. 

passed  between  two  aluminium  discs  C  and  D  supported  by  thin 
glass  rods  which  kept  them  a  constant  distance  apart.  Flexible 
wire  spirals  connected  these  electrodes  with  wires  sealed  through 
the  ends  of  the  tube.  A  piece  of  iron  H  was  fixed  to  the  frame 
carrying  the  electrodes  and  enabled  it  to  be  moved  along  the 
tube  by  means  of  a  magnet.  Two  electrodes  E,  F  about  1  mm. 

*  Hittorf,  Wied.  Ann.  xx.  p.  705,  1883. 

t  Graham,  Wied.  Ann.  Ixiv.  p.  49,  1898. 

J  A.  Herz,  Wied.  Ann.  liv.  p.  246,  1895. 

§  Skinner,  Wied.  Ann.  Ixviii.  p.  752,  1899. 

||  H.  A.  Wilson,  Phil.  Mag.  v.  49,  p.  505,  1900. 


227]         DISCHARGE  THROUGH   GASES  AT   LOW  PRESSURES.  435 

apart  were  fused  through  the  side  tube  G,  these  electrodes  were 
connected  with  a  quadrant  electrometer  whose  deflection  gave  the 
difference  of  potential  between  E  and  F,  and  hence  the  electric 
force  at  this  part  of  the  tube.  By  moving  the  framework,  EF 
could  be  brought  into  any  part  of  the  discharge  between  G  and  D, 
and  thus  the  distribution  of  electric  force  between  the  electrodes 
mapped  out.  Another  method  which  has  been  used  is  to  keep 
the  electrodes  C  and  D  fixed  and  move  E,  F  by  attaching  them  to 
a  support  floating  on  the  top  of  a  column  of  mercury  the  height  of 
which  could  be  altered. 

For  methods  such  as  those  just  described  to  be  successful  the 
secondary  electrodes  must  take  up  the  potential  of  the  gas  with 
which  they  are  in  contact ;  to  enable  them  to  do  this  quickly 
there  must  be  a  plentiful  supply  of  both  positive  and  negative 
ions  in  the  gas  which  by  giving  up  their  charges  to  the  wire  can 
raise  or  lower  its  potential  to  equality  with  the  surrounding 
gas ;  the  results  obtained  seem  to  justify  the  assumption  that  at 
moderate  pressures  the  secondary  electrodes  do  in  most  parts  of 
the  discharge  acquire  the  potential  of  the  gas,  but  the  method  is 
a  dangerous  one  when  the  pressure  is  very  low,  or  when  the 
wire  is  placed  in  the  Crookes  space  where  the  conductivity  is 
very  low. 

Thus,  to  take  an  extreme  case,  suppose  that  a  secondary 
electrode  is  placed  in  an  enclosure  in  which  there"  are  torrents 
of  negative  ions  but  no  positive  ones,  then  the  wire  will  go  on 
receiving  negative  electricity  until  it  gets  so  highly  charged  that 
it  is  able  to  repel  the  negative  ions  sufficiently  to  prevent  any 
more  striking  it ;  when  this  stage  is  arrived  at  its  potential  may 
be  lower  than  that  at  any  point  in  the  enclosure  previous  to  its 
introduction. 

227.  I  have  suggested  for  discharge  at  low  pressures  the  use 
of  a  method  in  which  the  deflection  of  the-  cathode  rays  is  used 
to  measure  the  strength  of  the  electric  field.  The  apparatus  used 
to  carry  out  this  method  is  shown  in  Fig.  127.  A  and  B  are 
the  electrodes  kept  at  a  constant  distance  apart  and  attached 
to  springs,  by  means  of  which  they  can  be  moved  along  the 
tube.  E  and  F  are  side  tubes  placed  in  line  with  each  other, 
in  E  cathode  rays  are  produced  by  a  Wimshurst  machine, 

28—2 


436 


DISCHARGE  THROUGH   GASES  AT   LOW  PRESSURES. 


[228 


a  pencil  of  these  rays  passes  through  a  small  hole  in  the  disc  G, 
traverses  the  electric  discharge  passing  between  A  and  B,  then 
travels  down  the  tube  F  producing  a  bright  patch  on  a  phos- 


B 


Fig.  127. 

phorescent  screen  placed  at  the  end  of  the  tube.  As  the  cathode 
rays  are  deflected  by  the  electric  force  along  the  line  of  discharge 
the  patch  on  the  screen  will  be  deflected  from  the  position  it 
occupies  when  the  discharge  is  not  passing ;  by  measuring  this 
deflection  we  can  determine  the  electric  force  at  the  part  of  the 
discharge  traversed  by  the  rays ;  by  moving  the  electrodes  A  and 
B  along  the  tube  we  can  map  out  the  electric  field  at  all  parts  of 
the  discharge.  Mr  Strachan  at  the  Cavendish  Laboratory  has  in 
this  way  obtained  the  distribution  of  electric  force  in  gases  at  low 
pressure. 

228.  The  distribution  of  electric  force  in  a  discharge  tube 
under  various  circumstances  as  to  pressure  and  current  is  repre- 
sented in.  the  following  figures  in  which  the  ordinates  represent 
the  value  of  the  electric  force  at  a  point  in  the  tube  whose  position 
is  fixed  by  the  abscissa.  From  these  curves  we  infer  that  the 
electric  force  is  very  large  indeed  in  the  Crookes  dark  space, 
diminishes  rapidly  towards  the  negative  glow,  and  in  the  negative 


228] 


DISCHARGE   THROUGH  GASES  AT   LOW  PRESSURES. 


437 


glow  itself  it  is  very  small ;  it  reaches  a  minimum  either  in  the 
glow  itself   or   in   the  portion  of  the   Faraday  dark  space  just 


& 


80 
70 
6o 
so 
40 

2o 

F^. 

N 

\ 

I 

\ 

V 

\ 

t 

+ 

-> 

/It 

\ 

QATI 

*L 

i. 

Pos 

T/V 

€     C 

/v 

O        1       7.       3      4-       5       6      7       8       9       10      II      1%      13    f+ 

Nitrogen.        Pressure  T06  mm.        Current  0*676  m.a. 
Fig.  128. 

outside  the  negative  glow,  after  which  it  increases,  towards  the  posi- 
tive column ;  in  the  case  of  a  uniformly  luminous  positive  column 
(Fig.  128)  the  electric  force  is  constant  along  it  until  we  get  quite 


70 

60 

S     so 

<s 

•?       40 

8, 

_       30 

\A 

C 

^    ^ 

s  r 

^ 

^ 

L/\ 

/\ 

5 
S     ao 

V 

\ 

1  0 

\ 

L. 

k.../-, 

fo 

.   .- 

S/f'J 
.'""! 

e  <:< 

/M,T 

.„ 

^ 

^f 

9«/>; 

t/^ 

J 

5123 
Hydrogen. 


4-5        6       7       8        9       'O      it      12     13      14-  Cms 

Pressure  2-25  mm.        Current  0-586  m.a. 
Fig.  129. 


close  to  the  positive  electrode ;  a  sudden  jump  in  the  potential 
called  the  anode  fall  of  potential  occurs  quite  close  to  the  anode  ; 
in  many  of  Wilson's  experiments  this  drop  was  preceded  by  the 


438 


DISCHARGE   THROUGH  GASES   AT   LOW   PRESSURES. 


[228 


electric  force  falling  to  an  exceedingly  low  value ;  in  some  cases 
indeed  it  was  apparently  reversed  ;  it  is  not  certain  however  that 
this  apparent  reversal  may  not  have  been  due  to  disturbances 
produced  by  the  introduction  of  the  wires,  &c.,  used  to  measure 
the  potential.  When  the  positive  column  was  striated  then,  as 
we  see  from  Fig.  129,  the  alternations  of  luminosity  in  the 
positive  column  are  accompanied  by  alternations  in  the  value  of 
the  electric  force,  maxima  of  the  electric  force  occurring  at  the 
bright  parts  of  the  striae,  minima  at  the  dark  parts.  Graham 


£- 

•X 

+f 

•»* 

\ 

\ 

1 

^ 

*^ 

* 

"s-—  « 

•> 

* 

^ 

1=-. 

^ 

J 

0         20         40         60         80        too          HO        '40        ilo         MO      70 

Fig.  130. 

showed  that  when  the  gas  was  impure  there  were  considerable 
variations  in  the  electric  force  even  in  the  luminous  positive 
column  ;  this  is  shown  in  Fig.  130  and  Fig.  131,  which  repre- 


1 

/ 

^ 

g 

\, 

> 

*x 

> 

1  —  i 

^ 

$ 

0          20         40          60        8O         loo        I'iO        /4p       I6o 

Fig.  131. 

il 

90 

1 

DQ 

sent  the  distribution  of  electric  force  in  an  impure  gas  and  in  one 
which  had  been  carefully  purified.     When  there  is  no  positive 


229]          DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.  439 

column  there  is  no  region  of  constant  intensity  between  the  anode 
and  the  negative  glow. 

If  X  is  the  electric  force,  supposed  parallel  to  x,  and  p  the 
density  of  the  electrification,  then  from  the  equation 

dX 


we  see  that  the  slope  of  the  curves  for  x  enables  us  to  find  the 
excess  of  the  positive  over  the  negative  ions  at  each  point  of  the 
discharge  ;  an  inspection  of  the  curves  shows  that  there  is  a  very 
large  excess  of  positive  over  negative  in  the  Crookes  dark  space  ; 
in  the  negative  glow  the  positive  and  negative  ions  are  about 
equal  in  number  ;  in  the  Faraday  dark  space  there  is  an  excess  of 
negative  ions  ;  in  the  uniform  positive  column  the  two  kinds  of 
ions  are  about  equal  in  number,  while  in  a  striated  positive 
column  there  is  a  negative  charge  on  the  cathode  side  of  the 
bright  part  of  a  striation  and  a  positive  charge  on  the  anode 
side. 

229.  Distribution  of  electric  force  near  the  cathode.,  The 
electric  field  in  the  neighbourhood  of  the  cathode  has  been  the 
subject  of  many  researches.  Hittorf  *  showed  that  the  potential 
difference  between  the  cathode  and  a  point  in  the  negative  glow  was 
independent  of  the  current,  provided  this  was  not  great  enough  to 
cause  the  negative  glow  to  enclose  the  whole  of  the  cathode.  When 
that  stage  was  reached  the  potential  between  the  cathode  and  the 
glow  increased  with  the  current.  Thus  if  the  cathode  is  a  wire, 
then  when  the  current  is  small  the  negative  glow  only  surrounds 
the  tip  of  the  wire  ;  as  the  current  is  increased  the  negative  glow 
encloses  more  and  more  of  the  wire,  but  it  is  not  until  the  glow 
reaches  the  end  of  the  cathode  that  the  difference  of  potertial 
between  the  cathode  and  the  glow  begins  to  be  affected  by  the 
current.  This  difference  of  potential  is  called  the  cathode  fall  of 
potential.  Warburg*)-  showed  that  it  was  independent  of  the  pres- 
sure of  the  gas,  and  that  the  potential  fall  was  practically  the  same 
whether  platinum,  zinc,  copper,  silver  or  iron  electrodes  were 
used  ;  it  was,  however,  considerably  less  when  the  electrodes  were 

*  Hittorf,  Wied.  Ann.  xx.  p.  705,  1883. 

t  Warburg,  Wied.  Ann.  xxxi.  p.  545,  1887  ;  xl.  p.  1,  1890. 


440  DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.          [229 

made  of  aluminium  or  magnesium.  Mey*  has  recently  shown 
that  the  cathode  fall  of  potential  depends  more  than  had  been 
thought  on  the  nature  of  the  cathode,  and  that  it  falls  to  com- 
paratively low  values  for  the  strongly  electro-positive  alkali  metals 
(see  also  Lyman,  Proc.  Camb.  Phil.  Soc.  xn.  p.  45,  1902).  With 
zinc,  copper  and  iron  electrodes  the  cathode  fall  of  potential 
is  often  abnormally  small  when  the  electrodes  are  new ;  it 
rises  however  to  its  normal  value  after  the  electrodes  have 
been  used  for  some  time.  Warburg  ascribes  this  effect  to  the 
presence  of  a  thin  layer  of  oxide  on  the  new  electrode,  which  gets 
removed  in  course  of  time  by  the  disintegration  which  occurs  when 
the  metal  is  used  as  a  cathode.  Hittorf-J-  discovered  that  the 
cathode  fall  became  exceedingly  small  when  the  cathode  was 
raised  to  a  red  heat.  Goldstein J  and  Warburg  (loc.  cit.)  found 
that  the  diminution  in  the  cathode  fall  became  much  less  when 
the  heating  was  continued  for  a  long  time.  It  is  worthy  of  remark 
in  this  connection  that  the  emission  of  negative  electricity  from 
an  incandescent  wire  often  falls  off  very  considerably  after  long- 
continued  heating.  Warburg  found  that  a  trace  of  impurity  in 
the  gas  produced  surprisingly  large  effects  on  the  cathode  fall  of 
potential.  Thus  he  found  that  the  cathode  fall  in  nitrogen  which 
contained  traces  of  moisture  and  oxygen  was  with  a  platinum 
cathode  260  volts,  while  the  same  nitrogen,  after  being  very  care- 
fully dried,  gave  a  cathode  fall  of  343  volts ;  thus  a  mere  trace  of 
moisture  had  diminished  the  cathode  fall  by  25  per  cent.  As  long 
as  the  total  quantity  of  water  vapour  is  small,  the  lowering  of  the 
cathode  fall  does  not  seem  to  depend  much  upon  the  amount  of 
aqueous  vapour  present;  when  however  there  is  much  water 
vapour  present  the  fall  is  greater  than  in  pure  nitrogen  ;  thus  in 
a  mixture  of  aqueous  vapour  and  nitrogen  in  which  the  pressure 
due  to  the  aqueous  vapour  was  2*3  mm.,  that  due  to  the  nitrogen 
3'9  mm.,  the  cathode  fall  was  396  as  against  343  in  nitrogen  with 
a  trace  of  oxygen ;  the  increase  in  the  cathode  fall  was,  however, 
not  nearly  so  great  as  that  in  the  potential  differences  along  the 
positive  column.  In  hydrogen  Warburg  found  that  a  trace  of 
aqueous  vapour  increased  the  cathode  fall  of  potential. 


*  Mey,  Verhand.  Deutschen  Physikalischen  Gesellschaft,  v.  p.  72,  1903. 
t  Hittorf,  Wied.  Ann.  xxi.  p.  133,  1884. 
t  Goldstein,  Wied.  Ann.  xxiv.  p.  91,  1885. 


229] 


DISCHARGE   THROUGH   GASES    AT   LOW   PRESSURES. 


441 


Warburg*  also  investigated  the  effect  of  removing  from  the 
gas  all  traces  of  oxygen.  This  was  done  by  depositing  on  the 
inside  of  the  tube  a  thin  layer  of  sodium,  which  was  produced  by 
placing  the  tube  in  sodium  amalgam,  heating  the  glass  and  sending 
a  current  of  electricity  from  the  amalgam  through  the  hot  glass  to 
an  electrode  inside  the  tube  :  the  sodium  thus  deposited  combined 
with  any  oxygen  there  might  be  in  the  tube.  The  removal  of  the 
oxygen  produced  a  very  great  effect  on  the  potential  fall ;  thus  in 
nitrogen  with  platinum  electrodes  the  cathode  fall  was  reduced  by 
the  removal  of  a  trace  of  oxygen  from  343  to  232  volts,  while  with 
magnesium  electrodes  the  cathode  fall  when  there  was  no  oxygen 
was  207  volts.  In  hydrogen  free  from  oxygen  the  cathode  fall  was 
300  with  platinum  electrodes  and  168  with  magnesium  electrodes ; 
thus  with  platinum  electrodes  the  cathode  fall  is  greater  in 
hydrogen  than  in  nitrogen  while  with  magnesium  electrodes  it  is 
less. 

The  following  table  contains  the  results  of  the  measurements  of 
the  cathode  fall  of  potential  in  various  gases  by  Warburg  (loc.  cit.), 
Capstickf  and  Strutt  J;  it  also  contains  the  measurements  by 


Gas 

Cathode  fall  in  volts 
Platinum  electrodes 

Cathode 
fall  with 
aluminium 
electrodes. 
WARBURG 

Minimum  po- 
tential differ- 
ence required 
to  produce  a 
spark.  STRUTT 

WARBURG 

CAPSTICK 

STRUTT 

Air  .. 

340—350 
about  300 

230  if  free 
from  0 
340 

298 
369 
232 

469 

582 

226 

168 
207 

341 
302—308 

251 
261—326 

H2    . 

02.. 

N2 

Hg  vapour 
Helium    .  .  . 
H'O  

NH3 

Strutt  of  the  least  potential  difference  able  to  produce  a  spark 
through  the  various  gases.  We  see  from  the  results  that  there  is 
very  considerable  evidence  in  favour  of  the  view  that  the  minimum 

*  Warburg,  Wied.  Ann.  xl.  p.  1,  1890. 

t  Capstick,  Proc.  Ray.  Soc.  Ixiii.  p.  356,  1898. 

J  Strutt,  Phil.  Tram,  cxciii.  p.  377,  1900. 


442 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


[230 


potential  difference  required  to  produce  a  spark  through  a  gas  is 
equal  to  the  cathode  fall  of  potential  in  that  gas. 

The  influence  of  the  material  of  the  electrode  is  shown  by  the 
results  quoted  in  the  following  table  which  is  due  to  Mey  (Lc.). 

CATHODE  FALL. 


Gas 

Electrode 

Pt 

Hg 

Ag 

Cu 

Fe 

Zn 

Al 

Mg 

Na 

Na-K 

K 

£:: 

&:: 

Arg.  . 

369 
300 
232 
226 
167 

226 

295 

280 

230 

213 

190 

168 

207 

185 

178 
80 

169 
125 

78-5 

172 

170 
69 

100 

• 

Capstick  found  that  if  in  dry  gases  a  trace  of  oxygen  was 
present  the  cathode  fall  was  approximately  the  same  as  in  pure 
oxygen.  This  is  borne  out  by  the  results  of  the  experiments  of 
Warburg  already  quoted  on  the  effect  produced  by  a  trace  of 
oxygen  in  the  presence  of  nitrogen.  When  water  vapour  is 
present  it  would  appear  from  Warburg's  experiments  that  this 
effect  of  the  oxygen  is  to  a  large  extent  neutralised.  We  have 
already  (p.  402)  alluded  to  Warburg's  experiments  on  the  great 
diminution  in  the  rate  of  escape  of  negative  electricity  from 
a  point  in  nitrogen  produced  by  the  presence  of  a  trace  of  oxygen  ; 
it  seems  probable  that  this  effect  is  connected  with  that  of  a  trace 
of  oxygen  on  the  cathode  fall.  The  latter  effect  can  hardly  be  due 
to  any  oxidation  of  the  electrode,  for  Warburg  has  shown  that  the 
potential  fall  at  slightly  oxidised  surfaces  is  less  than  that  at 
bright  ones. 

230.  For  the  compound  gases  H20  and  NH3,  the  only  ones 
hitherto  observed,  the  cathode  fall  seems  to  obey  the  additive 
law,  thus  the  cathode  fall  in  H20  =  cathode  fall  in  H2  +  J  cathode 
fall  in  02,  while  the  cathode  fall  in  NH3  =  J  cathode  fall  in 
N2  -f  |  cathode  fall  in  H2 ;  it  would  be  very  interesting  to  see  if  the 
connection  between  the  cathode  fall  in  a  gas  and  its  chemical 

o 

composition  suggested  by  the  two  results  just  quoted  is  confirmed 
by  further  observations  on  the  cathode  fall  in  other  compound 


231]          DISCHARGE   THROUGH   GASES  AT  LOW  PRESSURES.  443 

gases.  Carr  came  to  the  conclusion  that  the  minimum  spark 
potential  also  followed  the  additive  law.  The  experimental  diffi- 
culties are,  however,  very  great,  as  it  is  exceedingly  difficult  to 
get  a  continuous  discharge  through  a  compound  gas.  If  a  circuit 
containing  a  telephone  is  placed  in.  series  with  the  discharge  tube 
Capstick  found  that  it  is  almost  impossible  to  get  the  telephone 
silent  when  a  compound  gas  is  in  the  tube,  while  there  is  no  diffi- 
culty whatever  in  doing  so  with  an  elementary  gas.  The  singing 
of  the  telephone  indicates  that  the  discharge  is  intermittent,  and 
when  this  is  the  case  the  cathode  fall  cannot  be  measured. 

231.  Current  density  at  the  cathode.  H.  A.  Wilson*  has 
measured  the  current  density  at  a  cylindrical  wire  cathode  when 
the  negative  glow  does  not  envelope  the  whole  of  the  negative 
electrode.  Under  these  circumstances  the  glow  assumes  the  appear- 
ance shown  in  Fig.  132,  its  shape  resembling  a  test  tube  with  a  well 


TO     PUMP     ETC 


Fig.  132. 

marked  lip  at  the  end  furthest  from  the  anode;  as  the  current 
increases  the  glow  reaches  further  along  the  electrode,  the  length 
of  the  glow  being  proportional  to  the  current.  Wehneltf  has 
shown  that  the  discharge  from  the  cathode  is  confined  to  the  area 
covered  by  the  glow  and  that  the  current  density  is  constant  over 
this  area;  this  shows  that  the  current  density  at  the  cathode  is  inde- 
pendent of  the  total  current  flowing  through  the  tube,  provided 
that  this  is  not  so  large  as  to  make  the  glow  envelope  the  whole  of 
the  cathode.  Wilson  made  a  series  of  experiments  in  air  at  dif- 
ferent pressures,  ranging  from  6'7  mm.  to  "023  mm.,  and  found  that 
if  C  is  the  total  current  flowing  through  the  tube  in  milliamperes, 
I  the  length  of  wire  covered  by  the  glow  in  centimetres,  d  the 
diameter  of  the  wire  in  centimetres,  p  the  pressure  of  the  gas 
in  mm.  of  mercury,  then  C/l7r(d  +  'Q5)p  was  approximately  con- 
stant and  equal  to  '4 ;  this  result  indicates  that  the  current 
density  at  a  point  "25  mm.  from  the  surface  of  the  cathode  is 

*  H.  A.  Wilson,  Phil,  Mag.  vi.  4,  p.  608,  1902. 
t  Wehnelt,  Drude'-s  Ann.  vii.  p.  237,  1902. 


444 


DISCHARGE   THROUGH  GASES   AT  LOW   PRESSURES. 


[232 


constant  when  the  pressure  is  constant  whatever  the  diameter 
of  the  wire,  and  is  proportional  to  the  pressure  when  this  alters. 
It  is  remarkable  that  the  current  density  is  the  same  for  aluminium 
as  for  platinum  electrodes,  though  the  cathode  fall  is  different. 
An  inspection  of  Wilson's  numbers  shows  that  though  C/p  is 
approximately  constant  there  is  a  tendency  for  it  to  slowly 
decrease  to  a  minimum  and  then  slightly  increase  again. 

232.  The  distribution  of  electric  force  in  the  dark  space  and 
negative  glow.  The  first  determination  of  the  electric  force  in  the 
dark  space  was  made  by  Schuster*,  who  showed  that  if  V  is  the 
difference  of  potential  between  the  cathode  and  a  point  in  the 
dark  space  or  negative  glow  at  a  distance  x  from  the  cathode,  then 
the  relation 


where  F"0  is  the  cathode  fall  and  k  a  constant  (for  constant  pressure), 
represented  very  approximately  the   results  of  his   experiments. 


This  distribution  of  potential  would,  since  -^  =  —  4<7rp,  where  p 

(Lx 

is  the  density  of  the  free  electricity,  involve  in  the  dark  space  the 


30 


40 


20 


045 


0-2? 


o-o 


0       10     20     30  0       10     20      30     40 

Fig.  133. 

existence  of  a  positive  charge  of  electricity,  whose  density  de- 
creases, in  geometrical  progression  as  the  distance  from  the  cathode 
increases  in  arithmetical  progression. 

Graham -f-,  who  also  measured  the  distribution  of  the  electric 

*  Schuster,  Proc.  Roy.  Soc.  xlvii.  p.  526,  1890. 
t  Graham,  Wied.  Ann.  Ixiv.  p.  49,  1898. 


233] 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


445 


force  in  the  dark  space  near  the  cathode  in  nitrogen,  obtained 
for  the  distribution  of  potential  results  represented  by  the  curves 
in  Fig.  133.  From  these  curves  it  would  follow  that  although 
throughout  the  greater  part  of  the  dark  space  the  electrical  charge 
is  positive,  there  is  a  layer  of  negative  electricity  just  in  front  of 
the  cathode.  Wehnelt  has  repeated  Graham's  experiments  without 
finding  the  nicks  in  the  curve  near  the  cathode ;  he  ascribes  them 
to  the  two  exploring  wires  not  being  in  the  line  of  the  current. 
Wehnelt  gives  the  following  figures  as  representing  the  distribu- 


Fig.  134. 

tion  of  the  equipotential  surfaces  near  the  cathode  ;  they  probably 
are  influenced  to  some  extent  by  the  walls  of  the  tube.  Both 
Schuster  and  Graham  found  that  the  electric  force  increased  very 
rapidly  close  to  the  cathode ;  it  was  however  very  appreciable 
throughout  the  dark  space.  Skinner*,  in  some  recent  experi- 
ments, came  to  the  conclusion  that  the  whole  of  the  cathode 
fall  takes  place  quite'  close  to  the  cathode,  and  that  the  electric 
force  in  the  rest  of  the  dark  space  is  exceedingly  small.  I  think 
the  latter  result  must  be  due  to  the  exploring  wire  not  having 
taken  up  the  potential  of  the  gas  around  it ;  for  Strachan,  using 
the  method  described  on  page  436,  has  found  in  agreement  with 
Schuster  and  Graham  that  although  the  force  increases  exceedingly 
rapidly  near  the  cathode,  it  is  quite  appreciable  throughout  the 
rest  of  the  dark  space. 

233.     The  cathode  fall  of  potential  ceases  to  be  constant  when 
the  negative  glow  covers  the  whole  of  the  electrode,  or  when  it 

t  *  Skinner,  Phil.  Mag.  vi.  2,  p.  616,  1902. 


446  DISCHARGE  THROUGH  GASES   AT  LOW  PRESSURES.          [234 

reaches  to  the  walls  of  the  tube;  its  value  under  these  circumstances 
is  always  greater  than  the  normal  fall  and  may  rise  to  a  very  high 
value.  Stark*  has  given  the  following  formula  connecting  the 
cathode  fall  of  potential  K  with  the  intensity  of  the  current  when 
this  is  large  enough  to  cover  the  whole  of  the  cathode  with  negative 
glow 


where  Kn  is  the  normal  cathode  fall,  p  the  pressure  of  the  gas, 
f  the  area  of  the  cathode,  C  the  current  through  the  tube,  and  k 
and  x  constants. 

234.  Thickness  of  the  dark  space.  As  the  pressure  diminishes 
the  dark  space  gets  broader  and  broader  :  the  connection  between 
the  pressure  of  the  gas  and  the  width  of  the  dark  space  has  been 
investigated  by  Puluzf,  Crookesj,  and  more  recently  by  Ebert  §. 
According  to  Ebert  the  width  of  the  dark  space  is  not  in  general 
inversely  proportional  to  the  pressure  of  the  gas,  i.e.  directly 
proportional  to  the  mean  free  path  of  the  molecules  of  the  gas. 
The  law  found  by  Ebert  when  the  cathode  was  so  remote  from  the 
walls  of  the  tube  that  the  latter  did  not  exert  any  restriction  on 
the  growth  of  the  negative  glow  may  be  expressed  as  follows. 

Let  dl  ,  dj  be  the  thicknesses  of  the  dark  space  in  the  same  gas 
at  the  pressures  pl,  p2  respectively,  then 

d, 


where  m  is  a  positive  quantity  in  general  less  than  unity;  he 
found  that  for  the  gases  examined,  air,  O2,  H2,  N2,  CO,  and  C02, 
that  there  was  a  discontinuity  in  the  relation  between  d  and  p 
when  a  certain  pressure  II,  different  for  the  different  gases,  was 
reached,  the  value  of  m  for  pressures  greater  than  II  differing 
from  its  value  for  lower  pressures;  thus  to  take  oxygen  as  an 
example,  Ebert  found  that  for  pressures  greater  than  '7  mm.  of 
Hg  m  had  the  value  '459,  while  for  lower  pressures  m  was  equal 
to  '738.  It  is  remarkable  that  the  pressure  '7  mm.  is  the  pressure 

*  Stark,  Physikalische  Zeitschrift,  iii.  p.  274,  1902. 
t  Puluz,  Wien.  Sitz.  Ixxxi.  p.  874,  1880. 
£  Crookes,  Phil.  Trans,  clxx.  p.  138,  1879. 
§  Ebert,  Wied.  Ann.  Ixix.  pp.  200,  372,  1899. 


235] 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


447 


at  which  Bohr*,  Baly  and  Ramsay f  found  a  discontinuity  in  the 
relation  between  the  pressure  and  the  volume  of  the  gas  to  occur. 
Battellij  also  obtained  this  result.  Lord  Rayleigh§  who  made 
a  very  careful  examination  of  the  relation  between  the  pressure 
and  the  volume  of  oxygen  was  unable  to  detect  any  such  dis- 
continuity. Newalljl  discovered  that  the  electrodeless  discharge 
through  oxygen  behaved  very  differently  according  as  the  pres- 
sure was  greater  or  less  than  a  certain  critical  pressure  which 
was  about  '7  mm.  EbertIF  gives  the  following  values  for  II,  the 
pressure  at  which  the  change  in  the  law  connecting  p  and  d 
appears,  and  for  d  the  thickness  of  the  dark  space  at  a  pressure 
of  1  mm. 


Gas 

n 

d 

H9.. 

2'0  mm. 

3-8 

CO 

1*3  mm 

2-6 

N9 

1*0  mm 

2-2 

C09 

1*1  mm. 

2-1 

TT2    

Air    

0'9  mm. 

1-9 

0, 

0*7  mm 

1*6 

\^2  ••• 

He  states  that  II  is  approximately  proportional  to  the  reciprocal 
of  the  linear  dimensions  of  the  cathode ;  if  this  is  the  case  there 
seems  no  reason  for  connecting  II  with  the  stage  where  there  is 
a  change  in  the  relation  between  the  pressure  and  volume  of  the 
gas. 

235.  The  following  results  taken  from  Ebert's  paper  will 
give  some  idea  of  the  thickness  of  the  dark  space  d  at  different 
pressures  p  in  different  gases. 


p  in  mm.  of  Hg   I  2-06 
din  mm...  T2 


1-24 
1-8 


Air 

0-61  I  0-47 
2-4      3-1 


0-27 
4-6 


0-19 
7-0 


Oxygen 


p  I  1-18  I  0-73  I  0-45 

d  .,  1-64     2-09     2-93 


0-29 
4'16 


0-183  I  0-129  I    0-083 
5-48       7-69       10-43 


0-051 
14-3 


*  Bohr,  Wied.  Ann.  xxvii.  p.  459,  1886. 

f  Baly  and  Ramsay,  Phil.  Mag.  v.  38,  p.  307,  1894. 

$  Battelli,  Physikalische  Zeitschrift,  iii.  p.  17,  1901. 

§  Rayleigh,  Phil.  Trans.,  A.  196,  p.  205,  1901. 

||  Newall,  Proc.  Camb.  Phil.  Soc.,  ix.  p.  295,  1897. 

IT  Ebert,  Verhand.  Deutsch.  Physik.  Ges.  ii.  p.  99,  1900. 


448 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


[235 


Hydrogen 


p  in  mm.  of  Hg    I  3'05  I  2'04 
din  mm |  1-5    |  2'0 


1-37 

2-8 


0-95 
4-0 


Nitrogen 


2-85 
1-0 


1-91 
1-5 


1-25 
2-0 


0-82 
2-7 


0-72* 
5-0 


0-54* 
4-0 


0-54 
5-6 


0-35 
6-5 


0-40 
7-0 


0-26 
8-0 


The  results  for  hydrogen  and  nitrogen  are  plotted  in  Fig.  135, 
where  the  ordinates  represent  the  thickness  of  the  dark  space 
and  the  abscissae  the  reciprocals  of  the  pressure.  It  will  be  seen 
that  the  points  representing  the  experiments  at  the  higher  pres- 
sures lie  very  well  on  straight  lines,  while  at  lower  pressures  they 
no  longer  do  so.  The  pressures  when  the  curvature  becomes 
marked  are  close  to  the  pressures  called  by  Ebert  the  'critical 
pressure.'  He  found  that*  as  the  pressure  diminished  the  potential 


Fig.  135. 

difference  between  the  terminals  at  first  diminished  until  this 
critical  pressure  was  reached  ;  when  the  pressure  was  still  further 
reduced  the  potential  difference  increased  as  the  pressure  was 
diminished.  The  critical  pressure  was  found  to  depend  upon  the 
size  of  the  vessel,  the  larger  the  vessel  the  lower  the  critical  pressure. 
The  critical  pressure  marks  the  stage  when  the  walls  of  the  vessel 
begin  to  restrict  the  formation  of  the  glow  and  to  complicate  the 
phenomena.  In  studying  the  laws  governing  the  formation  of  the 
dark  space  it  is  better  to  confine  ourselves  to  pressures  higher 
than  the  critical  pressure,  when  the  walls  of  the  tube  do  not 
exert  any  influence.  Confining  our  attention  to  such  pressures 
I  am  inclined  to  interpret  Ebert's  experiments  somewhat  differ- 


235]          DISCHARGE   THROUGH   GASES    AT    LOW    PRESSURES.  449 

ently  from  Ebert  himself.  I  think  they  show  that  d,  the  thickness 
of  the  dark  space,  may  be  expressed  in  the  form 

6 

a  —  a  +  -  , 
P 

where  p  is  the  pressure,  and  a  and  b  are  constants.  If  X  is  the 
mean  free  path  of  a  molecule  of  the  gas,  X  is  proportional  to  1/jp, 
and  the  preceding  equation  may  be  written  in  the  form 

d  =  a  +  l3\ (1), 

or  the  dark  space  measured  from  a  distance  a  in  front  of  the 
cathode  is  proportional  to  the  mean  free  path  of  a  molecule  of  the 
gas.  If  we  plot  the  curve  in  which  the  ordinate  is  the  thickness 
of  the  dark  space  and  the  abscissa  the  mean  free  path  of  a  mole- 
cule of  the  gas,  then  taking  Xfor  nitrogen  at  atmospheric  pressure 
to  be  equal  to  9'86  x  10~6cm.  and  for  hydrogen  to  T85  x  10~5cm. 
(see  Meyer,  Kinetische  Theorie  der  Gase),  we  find  that  the  curves  for 
hydrogen  and  nitrogen  are  almost  identical ;  this  indicates  that  in 
equation  (1)  the  constants  a  and  /3  are  the  same  for  the  two  gases, 
i.e.  that  if  instead  of  measuring  the  dark  space  from  the  cathode 
itself  we  measure  it  from  a  constant  distance  from  the  cathode 
the  thickness  of  the  dark  space  bears  to  the  mean  free  path  of 
the  molecules  of  the  gas  a  ratio  which  is  the  same  for  all  gases. 
The  discharge  in  fact  behaves  as  if  the  negative  carriers  came 
from  a  region  a  little  in  front  of  the  cathode,  and  not  from  the 
cathode  itself.  H.  A.  Wilson's  experiments  on  the  current  density 
at  the  surface  of  the  cathode  suggest  the  same  view ;  the  value  of 
a,  the  constant  in  equation  (1)  as  given  by  the  curves  in  Fig.  135, 
is  about  '4  mm.  The  thickness  of  the  layer  at  the  surface,  of 
which  Wilson  found  the  current  density  to  be  constant,  is  in  air 
•25  mm. :  these  two  quantities  are  of  the  same  order,  and  we 
cannot  claim  for  the  value  of  a  as  determined  by  the  curve  in 
Fig.  135  any  great  accuracy,  as  a  slight  error  in  the  observations 
might  produce  a  large  percentage  error  in  a;  for  this  reason 
I  think  it  possible  that  the  identity  of  the  values  of  a  found  for 
hydrogen  and  nitrogen  may  be  partly  accidental,  and  more  experi- 
ments are  needed  before  it  can  be  considered  as  established  that 
a  is  the  same  for  all  gases.  It  would  be  interesting  to  see  if  the 
thickness  of  the  velvety  glow  which  covers  the  surface  of  the 
cathode  is  equal  to  a. 

T.  G.  29 


450  DISCHARGE   THROUGH    GASES   AT   LOW   PRESSURES.          [236 

Connection  between  the  thickness  of  the  dark  space  and  the  free 
path  of  a  corpuscle, 

236.  The  mean  free  path  of  a  hydrogen  molecule  at  0°  C. 
and  760mm.  pressure  is  1'85  x  10~5cm.  (Meyer,  Kinetische  Theorie 
der  Gase).  The  mean  free  path  of  a  corpuscle  will  be  greater  than 
this,  first  because  the  corpuscle  is  smaller  than  the  molecule ;  if 
for  the  sake  of  definiteness  we  take  the  view  that  the  collisions 
between  two  molecules  and  between  a  corpuscle  and  a  molecule 
are  analogous  to  those  between  two  elastic  spheres,  then,  neglect- 
ing the  radius  of  a  corpuscle  in  comparison  with  that  of  a  molecule, 
the  distance  between  the  centres  of  a  molecule  and  a  corpuscle 
when  in  collision  will  be  half  the  distance  between  the  centres  of 
two  molecules  when  in  collision.  Now  the  free  path  is  inversely 
proportional  to  the  square  of  the  distance  between  the  centres 
when  the  spheres  are  in  collision ;  thus  the  free  path  of  the 
corpuscle  will  be  four  times  that  of  the  molecule.  Again,  under 
the  electric  field  the  corpuscles  move  with  a  velocity  very  great 
compared  with  the  average  velocity  of  translation  of  the  molecules, 
so  that  the  latter  may  be  considered  to  be  at  rest.  Maxwell*  has 
shown  that  the  free  path  of  a  body  moving  through  a  collection 
of  molecules  at  rest  is  A/2  times  the  free  path  if  the  molecules 
were  moving  with  an  average  velocity  of  translation  equal  to  that 
of  the  moving  body;  thus  the  mean  free  path  of  a  corpuscle 
moving  through  hydrogen  at  0°  C.  and  760mm.  pressure  will  be 
4  \/2  x  1'85  x  10~5  cm. ;  the  free  path  at  a  pressure  of  Jxfnm.  will 
therefore  be  4  \/2  x  1*85  x  760  x  10-5cm.,  or  about  '8  of  a  milli- 
metre. The  thickness  of  the  dark  space  in  hydrogen  at  this 
pressure  reckoned  from  a  distance  '4  mm.  from  the  cathode  is 
about  3'3  mm.,  or  roughly  4  times  the  mean  free  path  of  the 
corpuscle,  and  we  have  seen  that  the  proportion  between  the 
thickness  of  the  dark  space  and  the  free  path  is  probably  the 
same  at  all  pressures  and  in  all  gases.  Thus  the  thickness  of  the 
dark  space  is  a  quantity  of  the  same  order  of  magnitude  as  the 
free  part  of  a  corpuscle  calculated  on  the  very  special  hypothesis 
used  above. 

Schuster*!"  found  that  the  thickness  of  the  dark  space  de- 
pended to  some  extent  on  the  current  passing  through  the  gas, 

*  Maxwell,  Collected  Papers,  vol.  i.  p.  386. 
+  Schuster,  Proc.  Roy.  Soc.  xlvii.  p.  556,  1890. 


237]          DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.  451 

increasing  slightly  with  an  increase  in  current.  Wehnelt*  on 
the  other  hand  found  that  the  dark  space  contracted  as  the 
current  increased ;  this  seems  to  indicate  that  the  dark  space  may 
have  a  stationary  value  for  some  particular  current,  increasing  or 
decreasing  with  the  current,  according  as  the  current  is  on  one 
side  or  the  other  of  this  particular  value. 

237.  Disintegration  of  the  cathode.  When  the  discharge 
passes  through  the  tube^portions  of  metal  shoot  out  normally  from 
the  cathode  and  form  a  thin  metallic  film  on  the  walls  of  the  tube 
or  any  body  in  the  neighbourhood  of  the  cathode;  indeed  thin  metal- 
lic films  for  serni-transparent  mirrors  are  now  frequently  made  by 
placing  a  piece  of  glass  in  a  vacuum  tube  near  a  cathode  made  of  the 
metal  it  is  wished  to  deposit  and  sending  a  current  through  the 
tube.  The  amount  of  metal  shot  off  from  the  cathode  depends  on 
the  pressure  of  the  gas  in  the  tube,  it  is  much  greater  at  low 
pressures  than  at  high.  It  depends  also  on  the  nature  of  the  gas; 
thus  there  is  very  little  disintegration  of  aluminium  electrodes  in 
air,  but  a  large  amount  in  the  monatornic  gases,  helium,  argdn  and 
mercury  vapour.  It  depends  largely  on  the  nature  of  the  metal. 
According  to  Crookes  f  the  order  of  the  metals  in  descending  order 
of  disintegration  is  Pd,  Au,  Ag,  Pb,  Sn,  Pt,  Cu,  Cd,  Ni,  In,  Fe. 
GranqvistJ  found  that  the  order  depended  on  the  pressure  of  the 
gas.  Thus  at  high  pressures  he  found  that  Pt  lost  more  than  Au, 
at  low  pressures  less.  His  results  showing  the  connection  between 
disintegration  and  pressure  are  represented  by  the  curves  in 
Fig.  136,  where  the  ordinates  are  the  loss  of  weight  in  milli- 
grammes in  an  hour  for  electrodes  12  mm.  long,  4'8  mm.  broad, 
and  '0(5  thick  when  a  current  of  2'46  milliamperes  passed 
through  the  tube,  and  the  abscissae  the  pressures.  Granqvist 
found  also  that  the  loss  in  weight  in  a  given  time  is  prop^r- 
tional  to  the  square  of  the  current  when  the  pressure  is  constant. 
Crookes  found  that  if  the  cathode  consisted  of  the  alloy  of  gold 
and  aluminium  discovered  by  Roberts- Austen  the  gold  was  de- 
posited while  the  aluminium  was  not ;  thus  the  composition  of  the 
cathode  was  changed  by  the  discharge.  The  amount  of  metal 
volatilised  from  a  cathode  is  very  much  greater  than  that  from 

*  Wehnelt,  Physikalische  Zeit.  ii.  p.  518,  1901. 

t  Crookes,  Proc.  Eoy.  Soc.  1.  p.  88,  1891. 

t  Granqvist,  Oefversigt.  Kgl.  Vetensk.  Akad.  Fork.  Stockholm,  1898,  p.  709. 

29—2 


452 


DISCHARGE   THROUGH  GASES  AT   LOW   PRESSURES. 


[238 


the  same  wire  when  incandescent;  thus  Granqvist*  found  that  he 
got  as  much  from  a  cathode  in  a  few  minutes  as  he  got  from  the 
same  wire  when  incandescent  and  without  charge,  or  when  used  as 


25 


10 


O  millimeCres 


t-0 
Fig.  136. 


/'£ 


20 


an  anode,  in  twelve  hours.  The  streams  of  metal  from  the  cathode 
are  deflected  by  a  magnet,  although  not  to  anything  like  the 
same  extent  as  the  cathode  rays. 

238.  The  cause  of  this  disintegration  of  the  cathode  has  not 
been  fully  determined ;  it  is  possible  that  it  is  due  to  the  same 
cause  as  the  disintegration  of  incandescent  wires,  a  very  thin  layer 
of  cathode  close  to  the  surface  being  in  a  state  analogous  to  that 
of  a  wire  at  a  very  high  temperature;  the  surface  of  the  cathode  is 
bombarded  by  the  positive  ions  which  have  fallen  through  a 
potential  equal  to  the  cathode  drop;  this  might  easily  raise  the 
surface  layers  to  such  a  temperature  that  the  energy  would  be 
radiated  away  and  would  not  escape  by  conduction  to  heat  the 
inside  of  the  cathode.  As  a  matter  of  fact  the  surface  of  the 
cathode  is  often  to  all  appearance  in  a  state  of  incandescence.  It 

*  Granqvist,  Kgl.  AJcad.  Stockholm,  liv.  p.  595,  1897. 


239] 


DISCHARGE    THROUGH  GASES  AT   LOW  PRESSURES. 


453 


would  be  interesting  to  test  this  view  by  seeing  if  the  presence  of 
even  a  trace  of  oxygen  increased  the  disintegration  of  the  cathode, 
as  it  produces  a  large  increase  in  that  of  an  incandescent  wire. 
I  am  inclined  to  think,  too,  that  gases  absorbed  in  the  metal  have 
a  considerable  effect  upon  the  disintegration  and  indeed  upon  the 
passage  of  the  electricity  from  the  cathode  to  the  metal ;  in  high 
vacua  the  potential  difference  between  an  anode  and  various 
cathodes  in  the  same  tube  will  often  change  capriciously,  the  order 
at  one  time  being  quite  different  from  that  a  few  minutes  later. 
This  would  be  readily  explained  if  the  amount  of  absorbed  gas 
influenced  the  potential  difference.  If  the  disintegration  does 
depend  on  absorbed  gas,  then  we  should  expect  the  rate  to  fall  off 
after  long-continued  use  of  a  cathode  in  a  high  vacuum. 

The  Faraday  dark  space  and  the  Positive  Column. 

239.  Measurements  of  the  electric  force  in  the  Faraday  dark 
space  were  first  made  by  Hittorf  *.  Graham  j*  and  H.  A.  Wilson J 
also  made  numerous  determinations  of  the  force  in  this  as  in  other 
parts  of  the  discharge,  while  Skinner  §  has  recently  investigated  the 
influence  of  pressure  and  of  the  magnitude  of  the  current  on  the 
force  in  the  dark  space  and  on  its  length.  The  results  of  Skinner's 
experiments,  which  were  made  on  carefully  purified  nitrogen, 


to      10      30     40      fO      do     Jo     90     9o      100     no     no     '50     ><* 
Millimetres. 
Fig.  137. 

and  with  disc    electrodes   of  considerable    area,  are   represented 
in  Fig.  137.     An  inspection  of  these  curves   shows  that   when 

*  Hittorf,  Wied.  Ann.  xx.  p.  705,  1883. 

t  Graham,  Wied.  Ann.  Ixiv.  p.  49,  1898. 

J  H.  A.  Wilson,  Phil.  Mag.  [5],  xlix.  p.  505,  1900. 

§  Skinner,  Phil.  Mag.  [5],  1.  p.  563,  1900. 


454  DISCHARGE  THROUGH   GASES   AT   LOW   PRESSURES.          [239 

the  pressure  is  kept  constant  the  width  of  the  dark  space 
increases  as  the  current  increases.  (The  boundaries  of  the  dark 
space  were  found  by  Skinner  to  be  at  the  points  corresponding  to 
the  intersection  of  the  straight  line  II  with  the  curves  giving  the 
electric  force.)  The  current  drives  as  it  were  the  luminous  positive 
column  back  on  the  anode,  until  with  the  largest  current  used  the 
luminous  positive  column  was  reduced  to  a  patch  close  to  the 
anode.  With  the  same  current  the  width  of  the  dark  space  is 
greater  at  low  pressures  than  at  high. 

Skinner  made  an  interesting  experiment  in  which  the  gas  in 
the  tube  was  shielded  from  any  disturbance  travelling  normally 
from  the  cathode.  The  cathode  was  a  disc  placed  with  its  plane  in 
the  axis  of  the  tube.  This  was  surrounded  by  a  piece  of  glass 
tubing,  the  axis  of  the  tube  being  at  right  angles  to  the  disc; 
thus  any  disturbance  travelling  from  the  cathode  at  right  angles  is 
prevented  from  reaching  any  but  a  small  part  of  the  gas  between 
the  electrodes.  With  this  apparatus  it  was  found  that  the 
luminous  positive  column  occupied  nearly  the  whole  of  the 
space  up  to  the  cathode :  the  dark  space  was  very  small,  and 
increased  but  little  with  an  increase  in  the  current.  Skinner 
observed  that  (with  a  tube  of  the  normal  type  with  the  electrodes 
facing  each  other)  when  once  by  means  of  a  large  current 
the  luminous  positive  column  had  been  driven  back  on  the 
anode,  the  gas  took  a  considerable  time  before  it  recovered  the 
power  of  transmitting  a  luminous  discharge ;  the  time  required 
for  the  recovery  depended  upon  the  time  the  large  current  had 
been  kept  flowing  through  the  tube.  Skinner  mentions  times 
of  one  or  two  hours  as  having  been  required  in  some  of  his 
experiments. 

The  potential  difference  between  the  electrodes  is  represented 
by  the  area  in  Fig.  137,  bounded  by  the -axis  of  abscissae,  the 
two  vertical  ordinates  through  the  electrodes,  and  the  curve 
representing  the  electric  force ;  we  see  from  an  inspection  of  the 
figure  that  this  area  diminishes  as  the  current  increases.  Thus 
the  curve  representing  the  relation  between  the  potential  dif- 
ference between  the  electrodes  and  the  current  through  the  tube 
slopes  downwards.  Hence  to  find  the  potential  difference  between 
the  electrodes  and  the  current  through  the  tube  when  an  external 
electromotive  force  E0  acts  on  a  circuit  including  the  tube,  we  pro- 


240]         DISCHARGE  THROUGH   GASES   AT  LOW  PRESSURES.  455 

ceed  as  in  Art.  222  by  drawing  the  line  y  —  E^  —  Rx,  where  R  is  the 
external  resistance  in  the  circuit,  and  finding  the  points  P,  Q  where 
this  line  cuts  in  the  curve  representing  the  relation  between  the 
potential  difference  and  the  current  through  the  tube.  For  the 
reason  given  in  Art.  222  the  point  P  to  the  left  corresponds  to 
an  unstable  state,  the  other  point  Q  to  the  stable  one.  Just  as 
in  the  case  of  the  arc  we  see  that  with  a  given  external  electro- 
motive force  the  current  through  the  tube  cannot  sink  below  a 
certain  finite  value  if  the  discharge  is  to  be  continuous*. 

Since  with  the  exception  of  the  cathode  dark  space  the  only 
dark  part  of  the  discharge  is  that  where  the  curve  representing 
the  electric  force  is  below  the  line  II  (Fig.  137),  it  follows  from 
Skinner's  experiment  that  there  is  luminosity  at  all  parts  of 
the  tube  (with  the  exception  of  the  cathode  dark  space),  when 
the  electric  force  exceeds  a  certain  value  depending  on  the 
pressure. 

The  Positive  Column. 

240.  The  potential  gradient  along  a  uniform  unstriated 
positive  column  is  uniform ;  its  value  has  been  investigated 
by  Hittorff,  A.  Herz]:,  Graham§,  Wiison||,  Skinnerlf.  The 
potential  gradient  in  the  positive  column  depends  (1)  upon  the 
diameter  of  the  discharge  tube,  (2)  upon  the  pressure  and  nature 
of  the  gas  through  which  the  discharge  is  passing,  and  (3)  the 
current  passing  through  the  gas. 

The  potential  gradient  diminishes  as  the  diameter  of  the 
discharge  tube  increases,  as  the  following  table  given  by  Herz 
(loc.  cit.)  shows.  The  influence  of  the  size  of  the  tube  is  not 
confined  to  tubes  which  are  so  narrow  that  their  diameter  is 
comparable  with  the  mean  free  path  of  the  molecules  and  cor- 
puscles in  the  tube,  but  extends  to  the  cases  when  the  diameter 
of  the  tube  is  hundreds  of  times  the  mean  free  path.  The  results 
in  the  table  relate  to  pure  nitrogen ;  v  is  the  potential  gradient  in 
volts  per  centimetre,  2R  the  diameter  of  the  tube  (the  current 

*  Kauffmann,  Drude's  Ann.  ii.  p.  158,  1900. 
t  Hittorf,  Wied.  Ann.  xx.  p.  726,  1883. 
J  Herz,  Wied.  Ann.  liv.  p.  244,  1895. 
§  Graham,  Wied.  Ann.  Ixiv.  p.  49,  1898. 

||  Wilson,  Phil.  Mag.  [5],  xlix.  p.  505,  1900 ;  Proc.  Camb.  Phil.  Soc.  xi.  pp.  249, 
391,  1902. 

IT  Skinner,  Phil.  Mag.  [6],  xi.  p.  616,  1901. 


456 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


[240 


passing  through  the  tube  was  in  all  cases  1*2  milliamperes),  p  is 
the  pressure  of  the  gas  expressed  in  millimetres  of  mercury,  and  b 
the  constant  occurring  in  the  equation 

v  —  v0  =  -  b  (i  —  i0), 

which  Herz  found  expressed  the  relation  between  the  gradients 
v  and  VQ  corresponding  to  the  currents  i  and  i0 ;  in  this  equation 
i  and  i0  are  expressed  in  milliamperes. 


i 

P 

2R  =  W  mm. 

2R  =  15  mm. 

,  2E  =  20  mm. 

2JR  =  25mm. 

8-0 

156-8 

7-5 

.  .. 

148-4 

7-0 

144-4 

140-1 

6-5 

139-2 

131-9 

, 

6-0 

132-6 

123-8 

5-5 

126-1 

115-8 

5-0 

118-2 

107-8 

4-5 

109-4 

99-9 

977 

4-0 

99-7 

92-2 

893 

3-5 

89-2 

84-5 

805 

3-0 

77-7 

76-1 

71-2 

2-5 

66-2 

615 

602 

2-0 

55-4 

51-4 

487 

1-5 

43-6 

40-8 

375 

I'O 

... 

29-8 

26-9 

b 

10-0 

8-5 

3-5 

3-4 

The  potential  gradient  in  the  positive  column  increases  with 
the  pressure,  the  results  of  Herz's  experiments  are  represented 
by  the  curves  in  Fig.  138  in  which  the  ordinates  represent  the 
potential  gradient  and  the  abscissae  the  pressure,  the  dotted  curve 
relates  to  experiments  with  hydrogen,  the  others  to  experiments 
with  nitrogen  in  tubes  of  different  dimensions,  the  curves  seem 
very  approximately  linear.  H.  A.  Wilson*  concluded  from  his 
experiments  that  the  potential  gradient  in  the  positive  column 
was  proportional  to  the  square  root  of  the  pressure ;  the  linear 
relation  v  —  a  +  bp,  where  v  is  the  potential  gradient,  p  the  pressure 


H.  A.  Wilson,  Proc.  Camb.  Phil.  Soc.  xi.  pp.  249,  391,  1902. 


242]          DISCHARGE   THROUGH   GASES   AT  LOW   PRESSURES.  457 

and  a  and  b  constants,  represents  the  results  of  his  experiments 
almost  equally  well. 


270 
Z40 
ZiO 

180 
(50 

12  0 
90 
60 

JO 
0 

2 

Rxy 

2«=/ 

;X 

/ 

x 

2/,a 

/^, 

x 

// 

/ 

, 

''" 

. 

x^r 

^ 

2o 

^  ' 

*^ 

fa 

f  ' 

'' 

^2 

«=2f 

-   ,' 

^ 

/ 

,' 

jf 

'  . 

''' 

*  , 

' 

—  ^ 

^ 

075       I'S       2'2ST    VO      375    45       S-2S    6-0       &-JS     -J-S      »25     9 

Fig.  138. 

Herz  showed  that  under  similar  conditions  as  to  pressure  and 
current  the  potential  gradient  in  nitrogen  was  1*4  times  that  in 
hydrogen.  He  found  that  a  trace  of  aqueous  vapour  had  no 
effect  upon  the  gradient  in  the  positive  column,  but  that  the 
presence  of  a  small  quantity  of  oxygen  in  the  nitrogen  increased 
the  potential  gradient. 

241.  Relation  between  the  potential  gradient  and  the  current. 
From   the   relation   v  —  v0  =  —  b  (i  — 10)   given    by  Herz   it   would 
follow  that  the  potential  gradient  in   the  positive  column  con- 
tinually increases  as  the  current  diminishes.     H.  A.  Wilson  has 
however   shown   recently  that  the   potential   gradient  attains  a 
maximum  value  for  a  certain  value  of  the  current  and  that  when 
the  current  falls  below  this  value  the  potential  gradient  rapidly 
diminishes. 

242.  When  the  positive  column  is  striated  the  variations  in  the 
luminosity  are  accompanied  by  variations  in  the  electric  intensity, 


458 


DISCHARGE  THROUGH   GASES   AT   LOW   PRESSURES. 


[243 


the  places  of  maximum  luminosity  are  places  of  maximum  poten- 
tial gradient,  this  is  clearly  shown  by  the  curve  in  Fig.  129,  which 
is  one  given  by  Wilson  for  the  striated  discharge  in  hydrogen. 

243.  Anode  drop  in  potential.  Skinner*  has  shown  that 
there  is  a  finite  difference  in  potential  between  the  anode  itself 
and  a  point  in  the  gas  close  to  the  anode.  The  magnitude  of 
this  drop  in  potential  was  investigated  by  him  for  the  discharge 
through  pure  nitrogen ;  he  found  that  it  was  independent  of  the 
current  density,  it  increased  slightly  with  the  pressure,  and  de- 
pended upon  the  metal  of  which  the  anode  was  made,  being 
greatest  for  aluminium  and  magnesium,  for  which  the  cathode 
fall  of  potential  is  least ;  the  value  of  the  anode  drop  at  different 
pressures  and  for  different  metals  is  represented  in  the  curves  in 
Fig.  139.  It  will  be  observed  that  the  anode  drop  is  much  smaller 


4-0 


30 


ro 


M 


0'5 


ro 


rs 


20 
Fig.  139. 


1'  5 


than  the  cathode  one,  it  is  also  much  more  abrupt;  there  does  not 
seem  any  region  comparable  in  dimensions  with  the  cathode  dark 
space  in  which  the  drop  of  potential  occurs;  in  none  of  the  ex- 
periments hitherto  made  has  it  been  found  possible  to  get  so 
close  to  the  anode  that  the  potential  of  the  exploring  wire  differed 
by  less  than  the  anode  fall  of  potential  from  the  potential  of  the 
anode. 


*  Skinner,  Wied.  Ann.  Ixviii.  p.  752,  1899. 


244] 


DISCHARGE   THROUGH   GASES   AT  LOW  PRESSURES. 


459 


There  is  frequently  a  region  in  which  the  electric  intensity  is 
very  small  just  in  front  of  the  anode;  in  some  of  the  experiments 
made  by  H.  A.  Wilson,  the  electric  intensity  was  apparently 
negative;  we  must  remember  that  the  introduction  of  the  ex- 
ploring wire  disturbs  the  field,  and  that  this  reversal  of  the 
electric  intensity  may  be  due  to  this  cause. 

244.  Number  of  ions  at  various  points  along  the  discharge. 
H.  A.  Wilson*  has  made  a  series  of  investigations  on  this  point; 
his  method  was  to  determine  the  current  flowing  between  two 
small  parallel  platinum  plates,  the  planes  of  the  plates  being 
parallel  to  the  current  flowing  through  the  tube,  a  small  potential 
difference  (that  due  to  one  Clark's  cell)  was  maintained  between 
the  plates,  previous  experiments  having  shown  that  with  potential 
differences  of  this  order  the  current  was  proportional  to  the 
potential  difference,  and  therefore  that  the  presence  of  a  field 
of  this  intensity  did  not  appreciably  reduce  the  number  of  free 
ions.  Under  these  circumstances  if  n^  n2  are  the  numbers  of 
positive  and  negative  ions  respectively,  klt  &2  the  velocities  of  these 
ions  under  unit  electric  force,  the  current  between  the  plates  is 
proportional  to  k^  +  k2n2.  The  results  of  Wilson's  experiments 


oeo 


0-15 


010 


o-c: 


0-20 


(NO 


0-05 


5      6       7       8       9       10      II       12      13 
Fig.   140. 

are  represented  in  Fig.  140.    It  will  be  noticed  that  the  current  is 
very  small  in  the  cathode  dark  space,  rises  to  its  maximum  value 

*  H.  A.  Wilson,  Phil.  Mag.  [5],  xlix.  p.  505,  1900. 


460  DISCHARGE  THROUGH   GASES  AT   LOW   PRESSURES.          [245 

in  the  negative  glow,  sinks  again  in  the  Faraday  dark  space  and 
increases  in  the  positive  column,  while  in  the  striated  discharge 
the  current  is  a  maximum  in  the  luminous  parts  of  a  striation, 
a  minimum  in  the  dark  ones. 

245.  It  is  interesting  to  compare  the  distribution  of  the 
electric  intensity  along  the  tube  with  these  transverse  currents.  If 
X  is  the  force  along  the  tube,  i  the  current  through  unit  area, 
and  if  the  velocity  of  the  ions  is  proportional  to  the  electric  force 
at  the  point,  then  we  have 

X  k 


as  i  is  constant  along  the  tube,  k^  +  k2n2  should  be  inversely 
proportional  to  X  ;  as  k^  +  k2n2  is  proportional  to  the  transverse 
current,  we  should  expect  the  maxima  for  the  transverse  current 
to  coincide  with  the  minima  for  X.  An  inspection  of  the  curves 
will  show  that  this  is  not  the  case;  thus  the  electric  intensity  in  the 
Faraday  dark  space  is  less  than  in  the  positive  column  ;  the  trans- 
verse current  is  also  less,  instead  of  being  greater  as  indicated 
by  the  preceding  reasoning.  Again,  both  the  electric  intensity 
and  the  transverse  current  are  greater  at  the  bright  parts  of  a 
striation  than  at  the  dark  ;  in  fact,  luminosity  seems  to  be  accom- 
panied by  abnormally  great  transverse  currents;  it  was  this  that 
led  H.  A.  Wilson  to  suggest  that  the  transverse  current  in  the 
luminous  parts  was  increased  by  secondary  ionisation  due  to  the 
illumination  of  the  testing  electrodes  by  the  luminosity  of  the 
discharge.  Skinner  has  suggested  as  another  explanation  for  the 
discrepancy  between  the  values  of  X  and  the  transverse  current 
that  the  velocity  of  the  ions  may  not  be  proportional  to  the 
electric  force  ;  that,  for  example,  though  the  electric  force  in 
the  Faraday  dark_jspace  is  very  small  the  ions  there  may  be 
moving  with  high  velocities  ,  which  they  acquired  in  moving 
through  the  strong  electric  field  in  the  cathode  dark  space  ;  thus 
the  number  of  free  ions  necessary  to  carry  the  current  may  be 
very  considerably  less  than  that  calculated  from  the  assumption 
that  the  velocity  was  that  due  to  the  electric  force  in  the  Faraday 
dark  space.  If  this  were  the  explanation  of  the  distribution  of 
the  transverse  force,  then  the  velocity  of  the  ions  in  the  Faraday 
dark  space  ought  to  be  greater  than  in  the  uniform  positive 
column.  Now  we  can  get  information  about  the  distribution  of 


245]          DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.  461 

the  velocity  of  the  ions  at  different  parts  of  the  tube  by  measur- 
ing the  '  Hall  effect.'  H.  A.  Wilson  *  has  shown  that  when  a 
magnetic  force  acts  at  right  angles  to  the  current  passing  through 
a  vacuum  tube,  then  a  difference  of  potential  proportional  to  the 
magnetic  force  is  established  between  two  electrodes,  placed  so 
that  the  line  joining  them  is  at  right  angles  both  to  the  current 
and  to  the  magnetic  force.  The  theory  of  this  effect,  called  the 
'Hall  effect/  has  been  given  in  Art.  115;  we  showed  that  when 
equal  quantities  of  positive  and  negative  ions  are  present,  then  if 
Z  be  the  difference  of  potential  between  two  electrodes  1  cm. 
apart  due  to  a  magnetic  force  H,  then 


where  u  and  v  are  respectively  the  velocities  of  the  negative  and 
positive  ions.  Thus  a  series  of  measurements  of  Z  along  the 
tube  will  enable  us  to  deduce  the  distribution  of  velocities; 


Transverse  force  in  volts  per  era.  for  constant  magnetic  field 

O  •  —  ro  <_w  -P*  C_n 

c 

A 

\ 

\ 

N^ 

i 

"-*- 

— 

^ 

\ 

r 

*^ 

4 

^< 

•^-x- 

^ 

-*  t 

i- 

2        34        56        789       10       II       12      13  cmz 

Positive  Column.                                Faraday  Dark  Space.       Negative 
Glow. 

Fig.  141.     Discharge  in  Air.     Pressure  0-5  mm.     Magnetic  Field  22-1. 

such  measurements  have  been  made  by  H.  A.  Wilson,  and   his 

results  are  represented  in  the  curves  given  in  Figs.  141  and  142. 

*  H.  A.  Wilson,  Proc.  Camb.  Phil.  Soc.  xi.  pp.  249,  391,  1902. 


462 


DISCHARGE   THROUGH   GASES  AT  LOW  PRESSURES. 


[245 


It  will  be  seen  that  the  curves  are  similar  in  character  to 
those  giving  the  distribution  of  electric  force ;  thus  the  value 
of  Z  in  the  Faraday  dark  space  is  less  than  in  the  positive  column, 


IJ 
12 
11 
10 
9 
8 
7 
6 
5 

4 
3 

a 
i 

( 

S 

jt 

/ 

* 

s 

*> 

*s 

2       1 

3  cms 

) 
i 

ft 

fegati 

*  —  ^ 

? 

ve 

-*— 
3       ^ 
Fara 

-x  — 

; 

lay  Da 

5       ( 
rkSps 

5 
ce. 

L 

7        ! 
S 

m. 

3  < 
tria. 

L 

?  i 

A 

0       1 
s 

E 

i  i 

tria. 

Glow. 
Fig.  142.     Discharge  in  Air.     Pressure  0-3  mm.     Magnetic  Field  29 '4. 

and  in  a  striated  discharge  Z,  like  X,  is  a  maximum  at  the  bright 
parts  of  the  striation,  a  minimum  at  the  dark.  These  results 
seem  to  indicate  that  though  a  certain  amount  of  lag  between  the 
values  of  X  and  the  velocity  of  the  ions  is  probable,  especially 
at  low  pressures,  it  is  not  sufficiently  large  to  explain  the  dis- 
crepancies between  the  curves  for  X  and  those  for  the  trans- 
verse currents. 

On  Wilson's  hypothesis  that  there  is  an  additional  ionisation 
due  to  the  incidence  of  the  light  from  the  discharge  on  the  metal 
of  the  electrodes,  the  current  between  electrodes  made  of  wire- 
gauze  might  be  expected  to  be  less  than  that  between  solid 
electrodes,  as  the  area  of  metal  exposed  to  the  light  is  so  much 
less  in  the  first  case  than  in  the  second. 


247]          DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES.  463 

246.  The  striated  discharge.    This  form  of  discharge,  examples 
of  which    are    represented   in    Fig.  125,   taken   from  papers   by 
De  la  Rue  and  Mtiller*,  has  from  its  very  striking  and  beautiful 
character  attracted  a  great  deal  of  attention.     It  only  occurs,  or  at 
any  rate  is  only  well  developed,  when  the  pressure  of  the  gas  and 
the  current  through  the  tube  are  within  certain  limits;  it  does 
not  however  depend  upon  the  means  used  to  produce  the  dis- 
charge ;  thus  we  get  striations  in  discharges  produced  by  induction 
coils,    electric  machines,   or  large  batteries  of  storage  or  voltaic 
cells. 

The  striations  are  especially  well  developed  in  mixed  gases, 
especially  those  which  contain  organic  vapours,  such  as  turpentine. 
Indeed  some  physicists  consider  they  would  not  occur  in  perfectly 
pure  gases  f ;  it  is  however  certain  that  they  occur  in  gases  which 
have  been  purified  with  the  greatest  care ;  according  to  Morren 
they  do  not  occur  in  oxygen.  Crookesj  observed  in  a  tube  con- 
taining hydrogen  three  sets  of  striations,  one  set  red,  another 
blue,  and  the  third  grey ;  by  spectroscopic  examination  he  showed 
that  the  luminosity  in  the  first  set  was  due  to  hydrogen,  that  in 
the  second  to  mercury  vapour,  and  that  in  the  third  to  hydro- 
carbons. It  will  be  noticed  from  Fig.  125  that  in  some  cases  the 
s.trise  seem  to  occur  in  sets  of  two  or  three  individual  striae 
situated  quite  close  together.  It  will  be  seen  that  the  luminous 
parts  of  the  striaB  are  curved ;  the  concavities  being  turned  to- 
wards the  positive  electrode.  When  the  tube  is  not  of  uniform 
width  the  striations  are  nearer  together  in  the  narrower  than  in 
the  broad  parts  of  the  tube. 

247.  Investigations  on  the  conditions  determining  the  distance 
between  successive  striations  have  been  made  by  Goldstein§,  and 
by  R.  S.  Willows||.     Goldstein  came  to  the  conclusion  that  if  d 
and  d0  were  the  distances  between  the  striations  at  the  pressures 
p  and  p0)  then 


*  De  la  Rue  and  Muller,  Phil.  Tram.  1878,  pt.  i.  p.  155. 

f  E.  C.  Baly,  Phil.  Mag.  xxxv.  p.  200,  1893. 

J  Sir  W.  Crookes,  Proc.  Roy.  Soc.  Ixix.  p.  399,  1902. 

§  Goldstein,  Wied.  Ann.  xv.  p.  277,  1882. 

II  Willows,  Proc.  Camb.  Phil.  Soc.  x.  p.  302,  1900. 


464 


DISCHARGE  THROUGH   GASES  AT   LOW  PRESSURES. 


[247 


where  m  is  a  quantity  less  than  unity  (compare  Art.  234).  The 
distance  between  the  striations  increases  as  the  pressure  diminishes, 
but  the  percentage  change  in  the  distance  is  not  so  great  as  that 
in  the  pressure. 

Willows  found  that  in  nitrogen  the  distance  between  the  striae 
increased  with  the  current.  Beginning  with  the  smallest  current 
capable  of  maintaining  the  discharge  the  distance  at  first  increased 
very  rapidly  with  the  current.  The  rate  of  increase  fell  off  how- 
ever as  the  current  increased ;  the  connection  between  the  current 
and  the  distance  between  the  striae  in  nitrogen  is  represented  by 
the  curve  in  Fig.  143. 


50 


70  90  110  130 

GA  L  .     D£fL  EX/ON 
Fig.  143. 


150 


170 


In  hydrogen  the  distance  between  the  striae  at  first  increases 
with  the  current;  it  then  attains  a  maximum,  and  then  any 
further  increase  in  the  current  produces  a  diminution  in  the 
distance  between  the  striae — the  lower  the  pressure  the  smaller 
the  current  for  which  the  distance  between  the  striae  is  a  maximum. 
At  very  low  pressures  this  current  may  be  very  little  larger  than 
the  smallest  current  consistent  with  a  continuous  discharge,  so 
that  at  these  pressures  the  phase  where  an  increase  in  current 
causes  the  striae  to  separate  may  be  almost  effaced.  The  relation 
between  the  current  and  the  distance  between  the  striae  for 
hydrogen  at  two  different  pressures  in  a  tube  12  mm.  in  diameter 
is  shown  in  Fig.  144.  The  terminals  for  curves  A  and  B  were 
aluminium  wires,  for  G  they  were  aluminium  discs. 


249] 


DISCHARGE    THROUGH    GASES    AT   LOW   PRESSURES. 


465 


By  comparing  these  results  with  those  for  the  thickness  of  the 
cathode  dark  space  we  see  that  under  similar  conditions  as  to 


pressure  and  current  the  distance  between  the  striae  is  considerably 
greater  than  the  thickness  of  the  dark  space. 

248.  Influence  of  the  size  of  the  discharge  tube.  The  wider  the 
tube  the  greater  the  distance  between  the  striae.  According  to 
Willows  (/.  c.)  this  distance  is  never  greater  than  the  diameter 
of  the  tube.  When  the  striae  reach  to  the  sides  of  the  tube 
Goldstein  showed  that  the  ratio  of  the  distances  between  the 
striae  for  two  given  pressures  is  independent  of  the  diameter  of 
the  tube.  Another  way  of  stating  Goldstein's  law  is  that  the 
constant  m  which  occurs  in  the  equation 


d.      p 

(see  Art.  247)  is  independent  of  the  size  of  the  tube. 

249.  Influence  of  the  nature  of  the  gas.  According  to  Willows 
the  distances  between  the  striae  in  different  gases  under  the  same 
conditions  as  to  pressure  and  current  are  not  very  different.  At 
pressures  between  1  mm.  and  '5  they  are  somewhat  further  apart 
in  hydrogen  than  in  air  or  nitrogen.  The  rate  of  alteration  of  the 
T.  a.  30 


466  DISCHARGE   THROUGH   GASES   AT  LOW   PRESSURES.          [250 

distance  with  the  pressure  is  however  greater  in  the  denser  gases 
than  in  hydrogen.  The  range  of  pressure  over  which  striations  can 
be  obtained  is  much  greater  in  hydrogen  than  in  air. 

250.  The  striae  are  most  readily  developed  at  the  negative 
end  of  the  positive  column.  Thus  if  the  pressure  be  gradually 
reduced  to  that  at  which  striation  occurs,  the  first  appearance  of 
striation  is  the  formation  of  a  single  stria  at  the  end  of  the 
positive  column.  Successive  striations  are  then  formed  until 
the  whole  of  the  positive  column  is  striated.  The  stria  at  the 
negative  end  of  the  positive  column  always  retains  some  indi- 
viduality; thus  its  distance  from  its  next  neighbour  is  greater 
than  the  average  distance  ;  it  is  also  often  brighter  than  the  other 
striaB. 


251.     Effect  of  a  sudden   contraction  in   the   discharge 
Goldstein*  found  that  in  a  tube  with  a  constriction,  such  as  that 
in  Fig.  145,  the  end  of  the  constriction  next  the  anode  behaved 


Fig.  145. 

like  a  cathode,  i.e.  that  there  was  a  dark  space,  negative  glow,  and 
Faraday  dark  space  close  to  a  ;  and  that  these  were  affected  by  a 
magnetic  field  in  just  the  same  way  as  if  they  had  been  produced 
by  a  metallic  cathode.  Lehmannf  made  a  series  of  experiments 
with  perforated  diaphragms  stretching  across  the  discharge  tube. 
He  found  on  the  side  of  the  diaphragm  next  the  anode  the 


Fig.  146. 

negative  glow  and  the  Faraday  dark  space  ;  the  cathode  dark 
space  was  however  absent.  In  the  experiment  represented  in  Fig. 
146  the  diaphragm  was  a  porcelain  sieve.  He  made  other  experi- 
ments with  tubes  having  several  perforated  metallic  diaphragms 

*  Goldstein,  Wied.  Ann.  xi.  p.  832,  1880. 
f  Lehmann,  Drud^s  Ann.  vii.  p.  1,  1902. 


252] 


DISCHARGE   THROUGH    GASES   AT   LOW   PRESSURES. 


467 


stretching  across  them.  These  diaphragms  were  connected  with 
wires  fused  through  the  tube  so  that  they  could  be  connected  up 
in  various  ways.  If  the  diaphragms  were  all  insulated  the  appear- 
ance of  the  discharge  was  as  represented  in  Fig.  146.  On  the 


t 


r 
4- 


c  h  c 

Fig.  147. 

anode  side  of  each  diaphragm  there  was  the  negative  glow  and 
the  Faraday  dark  space,  but  no  cathode  dark  space.  If  however 
two  of  the  diaphragms  were  connected  together  by  a  metallic  wire 
outside  the  tube,  as  Fig.  147,  there  was  negative  light  but  no  dark 
space  on  the  right  of  the  diaphragms  a  and  c ;  there  was  however 
a  well  defined  dark  space  on  the  right  of  b.  In  this  case  some  of 
the  current  instead  of  passing  through  the  tube  might  pass  through 
the  wire  outside,  and  at  b  would  have;  as  at  the  cathode  k,  to  pass 
from  the  metal  to  the  gas.  At  the  other  diaphragms  we  may 
suppose  the  current  went  through  the  holes  in  the  diaphragm. 

252.     Alternations  in  the  luminosity  of  the  discharge,  similar 


Fig.  148. 

in  appearance  to  those  observed  in  the  striated  positive  column 

30—2 


at 


468 


DISCHARGE   THROUGH   GASES   AT  LOW  PRESSURES. 


[253 


low  pressures,  occur  in  certain  cases  in  the  discharge  through  gas 
at  atmospheric  pressure.  Thus  Topler*  found  that  if  several 
large  Leyden  jars  were  discharged  across  a  spark  gap,  a  plate  of 
semi-insulating  material  such  as  basalt  being  inserted  between 
the  terminals,  the  portion  of  the  discharge  between  the  negative 
electrode  and  the  plate  showed  distinct  striations.  Fig.  148  is 
copied  from  a  figure  given  by  Topler.  The  discharge  of  an  in- 
duction coil  through  the  flame  of  a  candle  gives  a  bright  discharge 
traversed  by  dark  spaces  as  in  Fig.  149. 


Fig.  149. 

253.  Distribution  of  temperature  along  the  line  of  discharge. 
The  average  temperature  of  the  gas  in  a  discharge  tube  through 
which  a  luminous  discharge  is  passing  is  often  less  than  100°  C. 
Thus  E.  Wiedemannf  proved  that  the  average  temperature  of 
air  at  a  pressure  of  3  mm.  in  a  tube  conveying  a  luminous  dis- 
charge was  less  than  100°  C.  Hittorf  J  measured  the  temperature 
in  a  discharge  tube  at  three  places,  (1)  in  "the  positive  column, 

*  Topler,  Wied.  Ann.  Ixiii.  p.  109,  1897. 

f  E.  Wiedemann,  Wied.  Ann.  vi.  p.  298,  1879. 

J  Hittorf,  Wied.  Ann.  xxi.  p.  128,  1884. 


253] 


DISCHARGE   THROUGH   GASES   AT   LOW   PRESSURES. 


469 


(2)  in  the  negative  glow  and  (3)  in  the  Crookes  dark  space,  and 
found  that  it  was  highest  in  (3)  and  lowest  in  (1).  E.  Wiede- 
mann*  showed  that  the  distribution  of  temperature  along  the 
tube  depended  materially  upon  the  pressure,  and  that  while  at 
low  pressures  the  temperature  of  the  cathode  was  higher  than 
that  of  the  anode,  the  reverse  was  true  at  pressures  greater 
than  26  mm.  Woodf  made  a  very  complete  survey  of  the  tem- 
perature in  a  discharge  tube  by  means  of  a  bolometer,  which, 
floating  on  a  barometer  column  of  mercury,  could  be  placed  in 
any  position  in  the  tube.  He  found  that  in  the  unstriated  dis- 
charge .the  temperature  is  constant  in  the  positive  column, 
diminishes  in  the  Faraday  dark  space  until  it  reaches  a  minimum 
just  on  the  anode  side  of  the  negative  glow,  and  then  rapidly 
increases  in  the  dark  space  next  the  cathode.  In  the  striated 
discharge  the  temperature  is  greater  in  the  luminous  parts  than 
in  the  dark.  In  no  case  did  the  bolometer  indicate  a  temperature 
of  more  than  100°  C.  The  bolometer  temperature  is  of  course 
the  average  temperature  of  .all  the  molecules  in  a  considerable 
space,  and  the  fact  that  the  average  temperature  is  low  does 
not  preclude  a  few  of  the  molecules  possessing  an  amount  of 
kinetic  energy  very  much  greater  than  that  corresponding  to  the 


m- 


Fig.  150. 

temperature  indicated  by  the  bolometer.  The  distribution  of  tem- 
perature along  the  tube  in  a  striated  and  an  unstriated  discharge 
is  indicated  by  the  curves  in  Fig.  150.  It  will  be  seen  on  com- 

*  E.  Wiedemann,  Wied.  Ann.  x.  p.  202,  1880. 
t  Wood,  Wied.  Ann.  lix.  p.  238,  1896. 


470 


DISCHARGE   THROUGH  GASES  AT  LOW  PRESSURES. 


[254 


paring  these  with  the  curves  given  for  the  distribution  of  electric 
force  along  the  tube  that  the  two  curves  are  very  similar.  As 
the  rate  of  work  done  by  the  current  at  any  point  of  its  path  is 
proportional  to  the  product  of  the  current  and  the  electric  force, 
or  since  the  current  is  constant,  to  the  electric  force,  if  all  the 
work  were  converted  into  heat  the  curves  for  temperature  would 
be  similar  to  those  for  electric  force.  As  this  is  very  approximately 
the  case  we  conclude  that  in  tubes  of  moderate  pressure  the  greater 
part  of  the  electrical  work  appears  as  heat  in  the  gas  at  places 
not  very  distant  from  where  the  work  is  done. 

254.  Action  of  a  magnetic  field  on  the  discharge.  It  is  con- 
venient to  consider  separately  the  action  of  the  magnetic  force 
on  the  various  parts  of  the  discharge.  We  shall  begin  with  the 
negative  glow.  Pliicker*  showed  that  under  a  magnetic  field  the 
glow  distributed  itself  in  just  the  same  way  as  a  collection  of  iron 
filings,  having  perfect  freedom  of  motion ;  thus  the  bright  boundary 
of  the  negative  glow  coincides  with  the  lines  of  magnetic  force 
passing  through  the  end  of  the  negative  electrode.  This  effect  is 
illustrated  in  Figs.  151  and  152,  which  are  taken  from  Pliicker's 


Fig.  151. 

paper.  In  Fig.  151  the  lines  of  magnetic  force  are  transverse 
to  the  current,  while  in  Fig.  152  they  are  more  or  less  along  it. 
The  negative  glow  in,  fact  behaves  as  if  its  luminosity  were 

*  Pliicker,  Pogg.  Ann.  ciii.  p.  88,  1858. 


254] 


DISCHARGE   THROUGH   GASES   AT  LOW  PRESSURES. 


471 


produced    by   something    moving   along   the   lines   of    magnetic 
force.     If  the  direction  of  the  magnetic  force  is  along  the  line 


Fig.  152. 
of  discharge  the  negative  glow  spreads  further  down  the  tube 


Fig.  153. 

and  the  positive  column  is  driven  back;   if  the  magnetic  force 


Fig.  154. 

is  at  right  angles  to  the  tube,  the  negative  glow  follows  the  lines 
of  force  across  the  tube  and  does  not  extend  so  far  down  as  when 


472  DISCHARGE  THROUGH   GASES  AT   LOW   PRESSURES.         [255 

there  is  no  magnetic  field  ;  the  positive  column  now  comes  further 
down  the  tube  towards  the  cathode,  and  if  it  is  striated  new  stria- 
tions  appear.  These  effects  are  illustrated  by  Figs.  154  and  155, 


Fig.  155. 

which  are  due  to  Lehmann*.     Fig.  154  represents  the  case  when 
the  magnetic  force  is  along,  Fig.  155  when  it  is  across  the  tube. 

255.  Magnetic  force  affects  the  disposition  of  the  glow  over 
the  surface  of  the  cathode  as  well  as  its  course  through  the  gas. 
Thus  Hittorff  found  that  when  the  negative  electrode  is  a  flat 
vertical  disc  and  the  discharge  tube  is  placed  so  that  the  disc  lies 
axially  between  the  poles  of  a  strong  electromagnet,  the  disc  is 
cleared  of  glow  except  on  the  highest  point  on  the  side  most 
remote  from  the  anode  or  the  lowest  point  on  the  side  nearest  to 
it,  according  to  the  direction  of  the  magnetic  force.     In  another 
experiment  Hittorf,  using  as  cathode  a  metal  tube  about  1  cm.  in 
diameter,  found  that  when  the  axis  of  the  cathode  was  at  right 
angles  to  the  line  joining  the  poles  of  an  electromagnet  the  cathode 
was  cleared  of  glow  in  the  neighbourhood  of  the  places  where  the 
normals  are  at  right  angles  to  the  lines  of  magnetic  force.     Both 
these  results  are  what  we  should  expect  if  the  glow  were  due  to 
charged  particles  projected  normally  from  the  cathode.    The  effect 
of  a  magnetic  field  on  the  disposition  of  the  glow  over  the  cathode 
has  also  been  investigated  by  Schuster J. 

256.  The  positive  column  is  also  affected  by  the  magnetic 
field,  the  general  effect  being  that  the  column  is  bent  into  a  curve 

*  Lehmann,  Drude's  Ann.  vii.  p.  1,  1902. 
f  Hittorf,  Pogg.  Ann.  cxxxvi.  p.  221,  1869. 
Schuster,  Proc.  Roy.  Soc.  xxxvii.  p.  317,  1884. 


257]          DISCHARGE  THROUGH   GASES   AT   LOW  PRESSURES.  473 

resembling  the  path  of  a  positive  particle  under  the  action  of 
the  magnetic  field  and  the  electric  force  in  the  tube  (see  Art. 
40).  When  the  negative  glow  is  deflected  the  positive  column 
bends  towards  the  place  where  the  negative  glow  reaches  the 
walls  of  the  tube ;  this  effect  is  shown  in  Fig.  156,  which  is  due 
to  Lehmann.  There  is  often  a  dark  space  separating  the  ends  of 
the  negative  glow  and  the  positive  column,  as  if  the  area  of  contact 
of  the  former  with  the  glass  acted  like  a  secondary  cathode. 


Fig.  156. 

257.  Effect  of  magnetic  force  on  the  striations.  The  influence 
of  the  magnetic  field  on  the  striations  has  been  carefully  studied 
by  Spottiswoode  and  Moulton*,  and  by  Goldstein  f;  the  conclu- 
sion they  arrived  at  was  that  the  bright  parts  of  the  striations, 
like  the  negative  glow,  set  themselves  along  the  lines  of  magnetic 
force,  each  bright  part  setting  along  the  line  of  magnetic  force 
passing  through  it  and  being  separated  by  a  dark  space  from  its 
neighbour.  As  very  important  deductions  have  been  made  from 
this  behaviour  of  the  striae,  we  quote  the  description  of  this  effect 
given  by  Spottiswoode  and  Moulton  and  by  Goldstein.  The 
former  say  :  "  If  a  magnet  be  applied  to  a  striated  column  it  will 
be  found  that  the  column  is  not  simply  thrown  up  or  down  as  a 
whole,  as  would  be  the  case  if  the  discharge  passed  in  direct  lines 
from  terminal  to  terminal  threading  the  striae  in  its  passage.  On 
the  contrary,  each  stria  is  subjected  to  a  rotation  or  deformation  of 
exactly  the  same  character  as  would  be  caused  if  the  stria  marked 
the  termination  of  flexible  currents,  radiating  from  the  bright  head 
of  the  stria  behind  it  and  terminating  in  the  hazy  inner  surface 
of  the  stria  in  question.  An  examination  of  several  cases  has  led 
the  authors  of  this  paper  to  conclude  that  the  currents  do  thus 
radiate  from  the  bright  head  of  a  stria  to  the  inner  surface  of  the 
next,  and  that  there  is  no  direct  passage  from  one  terminal  of  the 

*  Spottiswoode  and  Moulton,  Phil.  Trans.  Part  i.  p.  205,  1879. 
t  Goldstein,  Wied.  Ann.  xi.  p.  850,  1880. 


474  DISCHARGE  THROUGH   GASES  AT   LOW   PRESSURES.          [258 

tube  to  the  other."  Goldstein  gives  the  following  description  of 
the  behaviour  of  the  striated  column  under  magnetic  force :  "  The 
appearance  is  very  characteristic  when  in  the  unmagnetized  con- 
dition, the  negative  glow  penetrates  beyond  the  first  striation  into 
the  positive  column.  The  end  of  the  negative  glow  is  then  further 
from  the  cathode  than  the  first  striation  or  even,  if  the  rarefaction 
is  suitable,  than  the  second  or  third.  Nevertheless  the  end  of  the 
negative  glow  rolls  itself  under  the  magnetic  action  up  to  the 
cathode  in  the  negative  curve  which  passes  through  the  cathode. 
Then  separated  from  this  by  a  dark  space  follows  on  the  side  of 
the  anode  a  curve  in  which  all  the  rays  of  the  first  striation  are 
rolled  up,  then  a  similar  curve  for  the  second  striation,  and  so  on." 
We  shall  have  occasion  to  refer  to  this  point  again  when  we 
consider  the  theory  of  the  discharge. 

258.  Paalzow  and  Neesen  *,  who  investigated  the  effect  of  a 
magnetic  field  in  helping  or  retarding  the  discharge,  found  that 
when  the  lines  of  force  are  parallel  to  the  line  of  discharge,  the 
nature  of  the  effect  depends  upon  pressure ;  if  p0  is  the  pressure 
at  which  the  discharge  first  begins,  pm  the  pressure  when  the 
current  through  the  tube  is  a  maximum,  and  pn  the  lowest 
pressure  at  which  the  discharge  passes,  then  for  pressures  be- 
tween p0  and  pm  the  magnetic  force  retards  the  discharge,  while 
if  the  pressure  is  between  pm  and  pn  it  helps  it ;  thus  the 
magnetic  field  produces  in  this  case  the  same  effect  as  an 
increase  in  pressure.  The  same  results  are  true  if  the  anode 
alone  is  exposed  to  the  magnetic  force;  if  only  the  cathode  is 
exposed  to  this  force  the  preceding  results  hold  if  the  field  is 
weak  ;  if  the  field  is  very  strong,  however,  the  effects  produced  are 
just  the  opposite,  the  magnetic  field  producing  the  same  effect  as 
a  diminution  in  pressure. 

When  the  lines  of  magnetic  force  are  at  right  angles  to  the 
discharge  the  magnetic  field  at  all  pressures  retards  the  discharge- 
They  found  that  the  effect  of  the  magnetic  field  was  not  instan- 
taneous, often  taking  several  seconds  before  producing  its  normal 
effect.  This  lag  is  a  very  frequent  phenomenon  in  the  discharge 
tube ;  it  generally  can  be  explained  by  the  effects  produced  by 
previous  sparks ;  thus  as  it  is  easier  for  one  discharge  to  .follow 

*  Paalzow  and  Neesen,  Wied.  Ann.  Ixiii.  p.  209,  1897. 


259]         DISCHARGE   THROUGH   GASES   AT  LOW   PRESSURES.  475 

another  than  to  be  the  first  to  pass  through  the  tube,  the  magnetic 
field  might  not  be  able  at  once  to  stop  the  discharge  if  a  strong 
discharge  had  just  previously  passed  through  the  tube,  though  it- 
might  be  able  to  prevent  a  discharge  starting  in  the  tube. 

The  author  showed  many  years  ago  that  the  passage  of  the 
electrodeless  discharge  was  hampered  by  a  transverse  magnetic 
field  and  facilitated  by  a  longitudinal  one. 

259.  Willows*,  who  also  investigated  the  effect  of  a  transverse 
magnetic  field  on  the  potential  difference  between  the  terminals 
of  a  discharge  tube  containing  gas  at  a  low  pressure,  found  that 
when  the  magnetic  force  is  confined  to  the  neighbourhood  of  the 
cathode  the  potential  difference  is  diminished  by  the  magnetic 
field  when  the  pressure  is  low  and  increased  when  it  is  high. 
The  effect  is  represented  in  the  curves  in  Fig.  157,  the  scale  of 


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Fig.  157. 

pressures  is  such  that  a  pressure  of  1  mm.  of  mercury  is  repre- 
sented by  223.  The  pressure  at  which  the  curve  for  the  magnet 
on  intersects  that  for  the  magnet  off,  increases  as  the  magnetic 
force  increases  and  decreases  when  the  current  through  the  tube 
decreases.  When  the  magnetic  force  is  concentrated  at  any 
part  of  the  tube  except  the  cathode  it  always  increases  the 
potential  difference. 

*  Willows,  Phil.  Mag.  vi.  1,  p.  250,  1901. 


476  DISCHARGE  THROUGH   GASES  AT  LOW   PRESSURES.          [260 

Willows  also  investigated  the  effect  of  a  uniform  transverse 
magnetic  field  on  the  distribution  of  electric  force  between  the 
terminals,  the  results  of  his  experiments  are  represented  by  the 
curves  in  Fig.  158  ;  the  magnetic  field  diminishes  to  a  considerable 
extent  the  great  drop  in  the  electric  force  which  occurs  in  the 
negative  glow. 


=  2'///nm. 


I 


Cathode 


Fig.  158. 


Anode 


260.  Birkeland*  has  shown  that  in  a  tube  containing  gas  at  a 
very  low  pressure  a  strong  magnetic  force  parallel  to  the  line  of  dis- 
charge produces  an  enormous  diminution  in  the  potential  difference 
required  to  spark  through  the  tube ;  the  potential  difference  when 
the  magnetic  force  at  the  cathode  reaches  a  critical  value  falling 
to  less  than  one-tenth  of  its  previous  value.  Almyf  has  shown 


*  Birkeland,  Comptes  Rendus,  cxxvi.  p.  586,  1898. 
t  Almy,  Proc.  Camb.  Phil.  Soc.  xi.  p.  183,  1901. 


262]          DISCHARGE  THROUGH  GASES   AT   LOW  PRESSURES.  477 

that  this  effect  can  be  produced  by  a  transverse  magnetic  force  as 
well  as  by  a  longitudinal  one,  and  that  the  sudden  diminution  in 
potential  is  accompanied  by  a  change  in  the  appearance  of  the 
discharge,  the  magnet  causing  the  discharge  to  change  from  a  form 
in  which  it  passes  from  the  whole  of  the  cathode  to  one  where 
it  is  concentrated  in  one  or  more  bright  streams.  This  change  in 
the  appearance  of  the  discharge,  and  also  the  diminution  in  the 
potential  difference  between  the  terminals,  can  be  produced 
without  the  aid  of  the  magnet  by  covering  the  outside  of  the 
tube  in  the  neighbourhood  of  the  cathode  with  tinfoil  connected 
with  the  cathode.  Almy  showed  that  the  effect  of  the  magnet  did 
not  arise  from  the  charges  of  statical  electricity  which  accumulate 
on  the  glass  of  the  tube,  by  showing  that  it  took  place  when  the 
cathode  was  placed  inside  a  metal  cylinder  which  was  used  as  the 
anode. 

261.  We  have  already  (see  p.  358)  described  the  appearance 
presented  by  the  discharge  when  the  terminals  are  placed  very 
near  together,  an  interesting  modification  of  such  an  experiment 
is  shown  in  Fig.  159,  which  represents  an  experiment  made  by 


Fig.  159. 

E.  Wiedemann*  in  which  the  anode  was  enclosed  in  a  narrow 
glass  tube  which  dipped  into  the  cathode  dark  space ;  it  will  be 
noticed  that  the  positive  light  turns  round  after  leaving  the  tube 
and  joins  the  negative  glow. 

262.  Discharge  produced  by  very  rapidly  alternating  electro- 
motive forces.  E.  Wiedemann  and  Ebertf  and  HimstedtJ  have 
made  some  very  interesting  experiments  when  the  discharge  was 
sent  through  the  tube  by  the  very  rapidly  alternating  forces 
produced  by  discharging  a  condenser;  in  Wiedemann  and  Ebert's 
experiments  the  terminals  were  connected  with  the  terminals  in 
a  Lecher's  bridge  arrangement  producing  electrical  oscillations 

*  E.  Wiedemann,  Wied.  Ann.  Ixiii.  p.  242,  1897. 

t  E.  Wiedemann  and  Ebert,  Wied.  Ann.  1.  pp.  1,  221,  1893. 

$  Himstedt,  Wied.  Ann.  lii.  p.  473,  1894. 


478  DISCHARGE   THROUGH  GASES  AT   LOW   PRESSURES.          [262 

whose  time  of  swing  was  only  about  10~8  seconds.  In  Himstedt's 
experiments  the  alternating  forces  were  produced  by  a  Tesla 
transformer.  The  appearance  presented  by  the  tube  is  shown 
in  Fig.  160 ;  it  will  be  seen  that  both  electrodes  show  only 
the  phenomena  associated  with  a  cathode,  i.e.  we  have  the  dark 
space,  the  negative  glow,  and  the  Faraday  dark  space,  but  no 


Fig.  160. 

positive  light ;  the  latter  is  represented  by  the  luminosity  in  the 
middle  of  the  tube ;  this  disappears  at  very  low  pressures.  The 
thickness  of  the  dark  space  next  the  electrode  diminishes  as  the 
rapidity  of  the  oscillations  increases. 


CHAPTER  XVI. 

THEORY  OF  THE  DISCHARGE  THROUGH  VACUUM  TUBES. 

263.  WE  shall  now  proceed  to  apply  the  theory  given  on 
p.  376  of  the  spark  discharge  to  explain  some  of  the  phenomena 
observed  when  the  discharge  passes  through  a  vacuum  tube  con- 
taining gas  at  a  low  pressure.  We  have  regarded  the  spark 
discharge  as  originating  in  the  ionisation  of  the  gas  by  moving 
ions,  the  small  negative  ions — the  corpuscles — being  more  efficient 
ionisers  than  the  positive  ones,  which  have  a  greater  mass.  If, 
however,  the  ionisation  in  an  electric  field  not  exposed  to  external 
ionising  agents,  such  as  Rontgen  rays,  were  solely  due  to  the 
collisions  of  corpuscles  with  the  molecules  of  the  gas  we  could  not 
have  a  continuous  current  through  the  gas.  For  suppose,  to  begin 
with,  there  were  a  few  corpuscles  between  the  electrodes,  then 
if  the  negative  electrode  is  on  the  right  the  electric  field  will  set 
the  corpuscles  moving  to  the  left,  and  if  it  were  strong  enough 
ionisation  would  occur  between  the  positive  electrode  and  the 
place  from  which  the  original  corpuscles  started.  The  new  cor- 
puscles produced  by  the  collisions  of  the  original  ones  with  the 
molecules  of  the  gas  would  themselves  produce  new  ions,  but  all 
these  would  be  formed  to  the  left  of  the  birth-place  of  the  ions 
which  produced  them,  there  would  thus  be  a  gradual  exodus  of 
corpuscles  towards  the  positive  electrode  while  the  gas  round 
the  negative  electrode  would  in  time  be  deprived  of  corpuscles 
and  would  cease  to  conduct,  and  by  hypothesis  it  could  no  longer  be 
ionised  as  all  the  negative  ions  would  have  been  driven  to  the 
positive  electrode. 


480  THEORY   OF   THE   DISCHARGE  [263 

We  have  seen  that  in  every  gas  'spontaneous'  ionisation  is 
continually  taking  place,  and  it  might  be  urged  that  this  process 
would  furnish  a  supply  of  negative  ions  which  would  rapidly 
multiply  by  collisions  with  the  molecules  of  the  gas,  and  so 
furnish  a  supply  of  carriers  sufficient  for  the  current  through 
the  tube.  If  this  were  the  case  however  the  potential  difference 
between  the  electrodes  would  vary  rapidly  with  the  current,  in 
reality  however  the  variation  is  very  slight. 

Again,  the  current  under  a  given  difference  of  potential  would 
depend  upon  the  amount  of  the  spontaneous  ionisation,  i.e.  the 
ionisation  independent  of  the  electric  field ;  we  can  however  increase 
the  latter  a  hundredfold  by  exposing  the  gas  in  the  discharge 
tube  to  the  action  of  Rontgen  rays  without  producing  any  appre- 
ciable increase  in  the  current  passing  through  the  gas.  To  account 
for  the  phenomena  of  the  discharge  we  must  have  ionisation 
produced  by  the  electric  field  itself  close  to  the  cathode;  we 
shall  suppose  that  this  ionisation  is  produced  by  the  positive, 
ions,  and  although  these  require  a  much  greater  amount  of  energy 
before  they  can  act  as  ionisers  than  do  the  corpuscles,  yet  the  very 
intense  electric  field  which  exists  close  to  the  cathode  is  sufficient 
to  give  them,  when  under  its  influence  they  have  come  up  to 
the  cathode,  all  the  energy  they  require. 

There  are  several  ways  in  which  these  rapidly  moving  positive 
ions  might  produce  fresh  negative  ions ;  the  two  that  most 
naturally  suggest  themselves  are,  (1)  that  the  positive  ions  by 
collision  ionise  the  molecules  of  the  gas  near  the  cathode,  (2)  that 
the  positive  ions  by  striking  against  the  surface  of  the  cathode 
communicate  so  much  energy  to  the  corpuscles  contained  in  the 
layer  of  metal  close  to  the  surface  of  the  cathode  that  they  are 
able  to  escape  from  the  metal,  just  as  they  are  able  to  escape  from 
a  metal  when  it  is  raised  to  incandescence. 

The  consequences  will  be  very  much  the  same  whichever  of 
these  views  we  take  ;  for  the  strength  of  the  electric  field  increases 
so  quickly  near  the  surface  of  the  cathode  that  the  kinetic  energy 
possessed  by  the  positive  ions,  when  they  arrive  quite  close  to  the 
surface,  will  be  enormously  greater  than  when  they  are  just  a 
little  further  off,  so  that  any  ionisation  produced  by  the  collision 
of  these  positive  ions  with  the  molecules  of  the  gas  will  be 
practically  confined  to  the  layer  of  gas  close  to  the  surface  of  the 


264]  THROUGH   VACUUM   TUBbiS.  481 

cathode.  It  is  possible  that  the  luminous  glow  which  spreads 
over  the  cathode  marks  the  seat  of  this  ionisation.  Thus  whether 
we  suppose  the  positive  ions  to  act  according  to  the  method  (1)  or 
(2)  we  have  negative  ions  starting  from  close  to  the  surface  of  the 
cathode ;  these  are  driven  from  it  by  the  electric  field  and  soon 
acquire  such  velocities  that  they  ionise  the  gas  through  which 
they  pass,  producing  a  supply  of  positive  ions  which  are  attracted 
by  the  electric  field  up  to  the  cathode,  there  to  produce  a  fresh 
supply  of  negative  ions. 

Thus  the  positive  and  negative  ions  in  the  space  close  to  the 
cathode  are  on  this  view  mutually  dependent;  if  the  supply  of 
either  is  stopped,  that  of  the  other  at  once  fails.  This  is  very  well 
illustrated  by  the  experiment  represented  in  Fig.  110,  p.  384,  in 
which  an  obstacle  placed  in  the  dark  space  throws  a  shadow  as  it 
were  backwards  and  forwards ;  the  obstacle  stops  the  supply  of 
positive  ions  to  a  portion  of  the  cathode  (the  portion  in  shadow); 
this  portion  is  no  longer  able  to  send  out  negative  ions,  in  fact 
it  ceases  to  act  as  an  electrode. 


Origin  of  the  dark  space. 

264.  Let  us  now  consider  in  more  detail  the  ionisation  pro- 
duced by  the  negative  ions  coming  from  the  cathode.  The  primary 
ones  which  start  from  or  near  the  surface  will  in  consequence  of 
the  very  intense  electric  field  which  exists  close  to  the  cathode  be 
shot  out  with  very  great  velocity,  they  will  therefore  be  cathode 
rays  of  a  very  penetrating  kind ;  such  rays  in  a  given  length  of 
path  do  not  produce  so  much  ionisation  as  those  moving  with  a 
smaller  velocity.  Let  us  now  consider  the  case  of  a  corpuscle 
produced  by  the  collision  of  one  of  the  primary  ones  with  a 
molecule  some  little  distance  in  front  of  the  cathode ;  this 
'  secondary '  corpuscle  will  start  from  a  field  much  less  intense 
than  that  from  which  the  primary  corpuscle  started,  it  will  therefore 
not  acquire  nearly  so  great  a  velocity;  it  will  correspond  to  a 
much  more  easily  absorbed  kind  of  cathode  ray,  and  will  therefore 
in  a  given  length  of  path  produce  many  more  ions.  Again,  the 
corpuscles  produced  by  the  '  secondary '  corpuscles  or  by  the 
primary  ones  at  a  greater  distance  from  the  cathode  will  in 
consequence  of  their  smaller  velocity  be  still  more  easily  absorbed, 
T.  G.  31 


482 


THEORY   OF   THE   DISCHARGE 


[265 


and  therefore  produce  still  more  ions  per  unit  of  path.  Thus  the 
amount  of  ionisation  will  be  small  in  the  strong  parts  of  the  field 
near  the  cathode,  but  will  increase  with  great  rapidity  when  we 
get  to  the  weaker  parts.  Thus  if  ionisation  were  accompanied  by 
luminosity  the  places  close  to  the  cathode  where  the  electric  field 
is  strong  would  be  dark,  while  the  luminosity  would  increase  with 
very  great  rapidity  in  the  places  more  remote  from  the  cathode 
where  the  electric  field  is  weaker :  the  increase  would  be  so  rapid 
that  the  contrast  and  line  of  demarcation  between  the  light  and 
dark  places  would  be  sharply  marked. 

265.  The  scarcity  of  the  negative  ions  in  the  strong  field  close 
to  the  cathode  and  their  rapid  increase  in  the  weaker  parts  of  the 
field  towards  the  negative  glow  are  strikingly  shown  in  some 


cathode 


Fig.  161. 


experiments  made  by  the  writer*.  In  these  a  discharge  tube  was 
used  similar  to  that  shown  in  Fig.  161,  G  is  a  floating  cathode 
which  can  be  raised  or  lowered  in  the  tube,  A  is  the  anode,  and  B 


J.  J.  Thomson,  Phil.  Mag.  vi.  1,  p.  361,  1901. 


265] 


THROUGH    VACUUM    TUBES. 


483 


a  closed  metal  vessel  provided  with  a  window  covered  with  very 
thin  aluminium  foil.  The  impact  of  negative  ions  on  this 
window  was  found  to  generate  rays  which  penetrated  the  tinfoil 
and  ionised  the  gas  in  the  closed  vessel.  This  gas  therefore 
conducted  electricity,  and  if  the  electrode  D  was  charged  and 
connected  with  an  electrometer,  the  charge  leaked  from  it,  the 
rate  of  leaking  indicating  the  amount  of  ionisation  in  the  gas, 
care  being  taken  to  charge  up  the  electrode  to  a  sufficiently  high 
potential  to  produce  the  saturation  current  through  the  gas.  The 
rays  are  very  easily  absorbed,  this  is  clearly  shown  by  diminishing 
the  pressure  of  the  gas  in  the  closed  vessel  B  and  observing  the  rate 
of  leak  at  different  pressures.  As  long  as  the  rays  are  entirely 
absorbed  in  passing  through  the  gas  in  the  vessel,  the  number  of 
ions  in  the  vessel,  and  therefore  the  saturation  current,  will  be 
independent  of  the  pressure  of  the  gas ;  as  soon  however  as  the 
pressure  gets  so  low  that  the  rays  pass  through  the  gas  without 
much  absorption,  the  saturation  current  becomes  proportional  to 
the  pressure.  The  following  table,  which  gives  the  variation  of 
the  saturation  current  with  the  pressure,  shows  that  it  is  not 
until  the  pressure  gets  low  that  the  saturation  current  is  affected 
by  the  pressure,  hence  we  conclude  that  the  radiation  produced 
by  the  impact  of  the  negative  ions  against  the  window  can 
only  penetrate  through  a  few  millimetres  of  air  at  atmospheric 
pressure  : 


Pressure  in  vessel  D 
(thickness  of  vessel  1  cm.  ) 

Saturation  current 

770  mm. 

87 

270     „ 

90 

100     „ 

64 

45     „ 

37 

10     „ 

11 

5     „ 

3 

The  intensity  of  the  rays  produced  by  these  negative  ions 
depends  very  much  upon  the  distance  of  the  window  from  the 
cathode.  This  is  clearly  shown  by  the  following  table,  the  results 
of  which  are  represented  by  the  curve  in  Fig.  162,  in  which  the 
ordinates  represent  the  amount  of  ionisation  in  the  vessel  and  the 
abscissae  the  distance  from  the  cathode. 

31—2 


484  THEORY   OF   THE   DISCHARGE  [265 

Pressure  in  discharge  tube  6  m.     Width  of  dark  space  6  mm. 


Distance  of  window  from 

lonisation  in  vessel  I) 

surface  of  cathode 

(arbitrary  units) 

3 

21 

4 

54 

5 

105 

6 

195 

8 

150? 

10 

180 

20 

66 

30 

40 

40 

25 

It  will  be  seen  that  the  effect  of  the  rays  produced  by  the  impact 
is  small  close  to  the  cathode,  increases  very  rapidly  as  we  approach 
the  negative  glow,  attains  a  maximum  in  the  glow,  and  then 


Fig.  162. 

quickly  drops  down  to  a  very  small  value ;  in  fact  the  effect 
produced  by  the  collision 'of  the  negative  ions  against  the  window 
varies  in  the  way  that  we  have  described  for  the  amount  of 
ionisation  produced  by  the  collision  of  the  corpuscles  with  the- 
molecules  of  the  gas. 


267]  THROUGH   VACUUM  TUBES.  485 

266.  The  fact  that  the  ionisation  inside  the  vessel  D  increases 
and  decreases  with  the  luminosity  in  the  discharge  might  lead  to 
the  suspicion  that  the  ionisation  inside  D  was  not  due  to  rays 
generated  by  the  impact  of  negative  ions  against  the  window,  but 
to  the  light  coming  from  the  gas ;  that  it  is  in  reality  due  to  the 
former  and  not  to  the  latter  cause  is  shown  by  the  following  experi- 
ment.    The  tube  was  placed  in  a  field  of  magnetic  force,  the  lines  of 
magnetic  force  being  parallel  to  the  window  in  the  box  D;  the 
magnetic  field  concentrates  the  negative  glow  and  increases  its 
luminosity,  so  that  if  the  ionisation  in  the  box  were  due  to  the 
luminosity  and  not  to  the  impact  it  should  be  increased  by  the 
magnetic  field ;  on  the  other  hand,  since  the  negative  ions  move 
parallel  to  the  lines  of  magnetic  force,  and  therefore  parallel  to 
the  window,  the  impact  of  the  ions  against  the  window  is  stopped, 
so  that  if  this  is  the  cause  of  the  ionisation  inside  the  box  it 
should   be   very  much    diminished  by  the   field ;    on  trying  the 
experiment  it  was  found  that  the  magnetic  field  almost  entirely 
stopped  the  ionisation. 

267.  On  the  theory  we  are  discussing  the  negative  glow  is 
due  to  the  ionisation  brought  about  by  collisions  between  mole- 
cules of  the  gas  and  corpuscles  which  have  started  some  distance 
from  the  cathode,  such  corpuscles  being  the  descendants,   so  to 
speak,  of  the  corpuscles  which  started  from  close  to  the  cathode 
and  which  move  with  very  much  greater  velocity  than  the  glow- 
producing    corpuscles    which    have    started   in    a    much   weaker 
electric  field.     The  thickness  of  the  dark  space  will  evidently  be 
greater  than  the  mean  free  path  of  a  corpuscle,  for  this  would  be 
the  approximate   magnitude   of  the   dark  space  if  the   negative 
glow   were  produced   by  collisions  with  the  corpuscles  from  the 
cathode;  the  greater  the  mean  free  path  the  further  will  the 
negative  glow  be  from  the  cathode,  and  we  should  expect  from 
the  preceding  theory  a  linear  relation  between  the  thickness  of  the 
dark  space  and  the  mean  free  path. 

The  corpuscles  which  start  from  close  to  the  cathode  being 
but  little  absorbed  may  sometimes  pass  right  through  the  negative 
glow,  as  in  the  case  of  the  discharge  studied  by  E.  Wiedemann 
and  represented  in  Fig.  124,  p.  432.  These  corpuscles  are  the 
cathode  rays  which  we  shall  discuss  in  the  next  chapter. 


486  THEORY   OF   THE   DISCHARGE  [268 

268.  When  ionisation  takes  place  in  the  region  round  the 
cathode  the  positive  ions  move  towards  the  cathode,  while  the 
negative  ones  move  away  from  it ;    this  produces  an   excess  of 
positive  electricity  in  the  gas  near  the  cathode.    In  consequence  of 
this  positive  charge  the  electric  force  diminishes  as  we  recede  from 
the  cathode.     When  the  electric  field  sinks  below  a  certain  value 
it  can  no  longer  communicate  to  the  corpuscles  sufficient  energy 
to  make  them  act  as  ionisers,  so  that  after  the  field  has  sunk  to 
this  value  the  ionisation  will  cease  ;  it  would  be  more  accurate  to 
say  that  the  ionisation  will  cease  soon  after  the  field  has  reached 
this  value,  for  the  corpuscles  may  retain  for  some  little  distance 
the  energy  they  acquired  in  stronger  parts  of  the  field  and  so 
continue  to  act  as  ionisers  for  a  short  distance  in  the  weak  field. 
The  limit  of  the  negative  glow,  furthest  from  the  cathode,  marks 
on  our  view  the  place  where  ionisation  ceases. 

269.  Let  us  now  consider  what   would   happen   in   the  gas 
between  the  anode  and  the  negative  glow  g.     Let  us  suppose  for 
a  moment  that  there  is  no  ionisation  taking  place  between  g  and 
the  anode.     Then  as  the  current  will  be  carried  by  ions  dragged 
by  the  electric  field  from  the  region  of  ionisation  between  g  and 
the  cathode,  all  the  ions  between  g  and  the  anode  will  be  negative 
ions,  so  that  there  will  be  a  negative  charge  in  the  gas  to  the 
left  of  g  ;  but  a  negative  charge  involves  an  increase  in  the  electric 
force  as  we  go  from  g  towards  the  anode,  and  if  the  anode  is  far 
enough  away  the  electric  field  may  increase  to  such  an  extent 
that  it  is  again  able  to  give  to  the  negative  corpuscles  sufficient 
kinetic  energy  to  make  them  ionisers.     When  this  happens  the 
gas  again  becomes  luminous,  and  we  have  in  fact  a  repetition  of 
the  process  occurring  in  the  negative  glow.     The  increased  ionisa- 
tion in  the   luminous  part   of  the   discharge  will   diminish  the 
strength  of  the  electric  field  until  this  gets  so  weak  that  no  further 
ionisation  takes  place,  the  luminosity  again  ceases  and  the  current 
will  again,  as  in  the  Faraday  dark  space,  be  carried  by  ions  pro- 
duced elsewhere;  there  will  also,  as  in  that  space,  be  an  excess  of 
negative  ions,  this  will  cause  the  electric  force  again  to  increase, 
ionisation  accompanied  by  luminosity  will  recur,  and  the  process 
will  be  repeated  right  up  to  the  anode ;  we  thus  get  bright  and 
dark  patches  as  in  the  striated  positive  column.    On  this  view  the 
luminous  portions  of  the  striations  correspond  to  the  negative 


270]  THROUGH   VACUUM  TUBES.  487 

glow,  the  intervening  dark  spaces  to  the  Faraday  dark  space,  the 
process  taking  place  along  the  positive  column  being  a  repetition 
of  that  taking  place  near  the  cathode.  The  similarity  between 
the  striated  positive  column  and  the  phenomena  at  the  cathode  has 
been  insisted  on  by  several  observers,  notably  by  Spottiswoode  and 
Moulton*,  Goldstein -f-5  and  LehmannJ.  Goldstein's  statement  is 
very  clear  and  explicit,  he  says,  "  Jede  einzelne  Schicht  des  posi- 
tiven  Lichtes  ist  ein  dem  frtiher  sogenannten  negativen  oder 
Kathodenlichte  entsprechendes  Gebilde,  und  das  geschichtete 
positive  Licht  besteht  eigentlich  aus  einer  Aufeinanderfolge  von 
Komplexen  negativen  Lichtes §."  Several  observers  have  regarded 
the  behaviour  of  the  positive  column  as  necessarily  implying  a 
discontinuity  in  the  discharge.  Thus  Spottiswoode  and  Moulton 
from  the  behaviour  of  the  striated  column  liken  the  transmission 
of  electricity  along  the  positive  column  "to  an  action  consisting 
of  an  independent  discharge  from  one  stria  to  the  next,  and  the 
idea  of  this  action  can  perhaps  be  best  illustrated  by  that  of  a  line 
of  boys  crossing  a  brook  on  stepping  stones,  each  boy  stepping  on 
to  the  stone  the  boy  in  front  of  him  has  left."  On  the  view  we 
have  indicated  above  a  striated  discharge  need  not  necessarily  be 
discontinuous. 

270.  We  saw  in  Art.  35  that  when  the  velocity  of  the  ions 
is  proportional  to  the  electric  force  the  curve  representing  the 
relation  between  the  electric  force  at  a  point  and  the  distance  of 
that  point  from  one  of  the  electrodes  is  convex  to  the  axis  when 
the  ionisation  in  the  gas  is  greater  than  the  recombination  of  the 
ions,  and  concave  when  it  is  less.  The  curve  representing  the 
distribution  of  electric  force  along  the  striated  positive  column  is 
however  (see  Fig.  129)  concave  at  the  bright  parts  of  the  striae 
where  we  have  supposed  the  ionisation  to  be  greatest,  and  convex 
at  the  dark  parts  where  the  ionisation  is  least.  In  a  case,  however, 
like  that  of  a  striated  discharge  where  the  pressure  of  the  gas  is 
low,  and  the  free  path  of  a  corpuscle  therefore  considerable,  the 
velocity  of  a  corpuscle  at  a  point  will  depend  not  only  upon 
the  magnitude  of  the  electric  force  at  that  point,  but  also  upon 
the  forces  which  acted  upon  it  before  it  reached  the  point :  thus 

*  Spottiswoode  and  Moulton,  Phil.  Trans.  Part  i.  p.  205,  1879. 

t  Goldstein,  Wied.  Ann.  xi.  p.  831,  1880;  xii.  pp.  90,  249,  1881. 

£  Lehmann,  Die  Elektrischen  Entladungen. 

§  Goldstein,  Berlin.  Monatsber.  May  4,  1876. 


488  THEORY    OF   THE    DISCHARGE  [271 

the  conditions  upon  which  the  investigation  in  Art.  35  is  based 
need  not  apply  in  this  case. 

271.  Case  when  the  discharge  is  not  striated  and  the  positive 
column  is  of  uniform  intensity.     The  corpuscles  are  continually  re- 
combining,  so  that  unless  there  is  fresh  ionisation  their  number  is 
continually  diminishing :  if  the  rate  of  ionisation  is  equal  to  that 
of  recombination  the  number  of  corpuscles  will  remain  constant. 
Thus  if,  when  the  ionisation  begins  at  the  anode  end  of  the  Faraday 
dark  space,  the  strength  of  the  field  is  such  that  the  number  of 
ions  produced  by  it  in  unit  time  is  just  equal  to  the  number  which 
recombine  in  that  time,  the  number  of  ions,  the  strength  of  the 
field,  the  amount  of  ionisation,  and  therefore  the  luminosity  will 
be  constant  all  along  the  line  of  discharge,  and  we  shall  have  the 
case  of  the  uniform  positive  column. 

272.  Anode  fall  of  potential.     Let  us  consider  a  point  P  close 
to  the  anode  A,  then  the  current  at  P  is  carried  by  negative 
corpuscles  produced  further  from  the  anode  than  P  and  by  positive 
ions  either  coming  out  of  the  anode  or  produced   from  the  gas 
between  P  and  A.     That  a  considerable  supply  of  positive  ions 
is  produced  within  a  short  distance  of  the  anode  is  proved  by  the 
fact  that  in  the  uniform    positive  column  the   electric  force   is 
constant  within  a  short  distance  of  the  anode,  and  when  this  is  the 
case  there  are  as  many  positive  as  negative  ions  per  unit  volume' 
of  the  gas.    Thus  if  the  ions  are  produced  in  the  gas  the  ionisation 
in  the  gas  near  the  anode  must  be  so  intense  that  in  an  exceed- 
ingly thin  layer  of  gas  there  are  sufficient  positive  ions  produced 
to  neutralise  the  electrostatic  effect  of  the  negative  ones  moving 
up  to  the  anode.     Now  under  these  conditions,  if  i  is  the  current, 
Rl}  R2  the  velocities  of  the  positive  and  negative  ions  respectively, 
the  number  of  positive  ions  which  cross  unit  area  of  the  uniform 
positive  column  in  unit  time  is  Rlil(Rl  +  R2)  e,  where  e  is  the 
charge  on  an  ion.     Suppose  w  is  the  work  required  to  ionise  a 
molecule  of  the  gas,  then  in  the  thin  layer  referred  to  an  amount 
of  work  equal  to  wRli/(Rl  +  R2)e  must  be  done  by  the  electrical 
field  in  unit  time ;  but  if  V  is  the  difference  of  potential  between 
the  two  sides  of  this  layer  (one  of  these  sides  is  the  anode),  the 
electrical  work  done  in  unit  time  is    VR2i/(Rj  +  R.2),  since  the 
quantity  of  negative  electricity  entering  this  layer  in  unit  time 


273]  THROUGH  VACUUM  TUBES.  489 

is  R.2i/(Rl  +  R.2);  hence  supposing  all  the  electrical  work  is  spent 
in  ionising  the  gas,  we  have 

VR2i  R,wi 


or  e  —  -^w] 

Mz 

this  is  an  inferior  limit  to  F,  since  it  is  obtained  on  the  assumption 
that  all  the  work  is  spent  in  ionising  the  gas  :  we  have  thus  a 
finite  drop  in  the  potential  at  the  anode.  If  we  proceed  on  the 
other  supposition,  that  the  positive  ions  come  from  the  anode,  just 
as  we  have  seen  positive  ions  do  come  out  of  metal  or  out  of  the 
gases  absorbed  by  metal  when  the  temperature  is  above  a  dull 
red  heat,  the  preceding  investigation  will  still  apply,  if  10  stands 
for  the  energy  required  to  eject  an  ion  from  the  metal,  so  that 
in  this  case  again  there  is  a  finite  drop  of  potential  at  the 
anode. 

273.  Action  of  magnetic  force  upon  tJie  discharge.  We  have 
seen  (see  Art.  40)  that  when  a  charged  particle  moving  through  a 
gas  is  acted  upon  by  both  electric  and  magnetic  forces,  it  will  follow 
the  lines  of  magnetic  and  not  of  electric  force,  provided  RH  is  a 
large  quantity  ;  here  H  is  the  magnetic  force,  and  R  the  velocity 
acquired  by  an  ion  under  unit  electric  force.  Another  way  of  ex- 
pressing the  same  result  is  to  say  that  a  charged  particle,  moving 
with  the  velocity  v,  will  follow  the  lines  of  magnetic  force  if  mv/eH, 
the  radius  of  the  circle  into  which  the  path  of  a  free  particle 
is  bent  when  moving  at  right  angles  to  the  magnetic  force,  is 
small  compared  with  the  mean  free  path  of  the  particle.  The 
result  when  put  in  this  form  is  obvious,  since  (see  p.  82)  the  free 
paths  of  the  particles  are  spirals  round  the  lines  of  magnetic 
force,  and  as  the  radii  of  these  spirals  are  small  compared  with 
the  length  of  the  mean  free  path  the  only  direction  in  which 
the  particles  make  any  appreciable  progress  is  that  of  the  mag- 
netic force.  The  negative  particles  will  be  much  more  likely  than 
the  positive  to  follow  the  lines  of  magnetic  force  ;  for  in  the  first 
place,  the  mean  free  path  of  the  negative  particles  is  greater  than 
that  of  the  positive,  and  secondly,  the  value  of  m/e  is  much  less 
for  the  negative  than  for  the  positive  particles.  Thus  we  may 
expect  the  negative  particles  to  follow  the  lines  of  magnetic  force, 


490  THEORY   OF   THE   DISCHARGE  [274 

even  when  the  motion  of  the  positive  ones  is  but  little  affected 
by  the  magnetic  field.  The  tendency  of  the  negative  particles 
to  follow  the  lines  of  magnetic  force  is  strikingly  shown  by  the 
behaviour  of  the  negative  glow  in  a  strong  magnetic  field,  when, 
as  Pllicker  has  shown  (see  p.  470),  the  boundary  of  the  glow 
coincides  with  a  line  of  magnetic  force. 

274.  Since   the  negative   particles  are  much  more  affected 
than  the  positive  by  a  magnetic  field,  if  the  proportion  of  the 
current  carried  by  the  negative  ions  varies  at  different  points  in  its 
course  the  current  will  be  much  more  deflected  by  the  magnetic 
field  in  some  places  than  in  others.     This  is  exactly  what  happens 
in  the  striated  discharge;  for  "suppose  A  and  B  are 'the  bright 
parts  of  two  consecutive  striae,  then  since  by  hypothesis  there  is 
ionisation  in  A,  many  more  negative  particles  will  leave  A  from  the 
anode  side  than  enter  it  from  the  cathode  side ;  thus  the  proportion 
of  the  current  carried  by  the  negative  ions  will  be  much  greater 
on  the  anode   side   of  the  bright  patches  than  on  the  cathode 
side  ;   the  portion  of  the  current  on  the  anode  side  of  a  bright 
patch  will  therefore  be  much  more  affected  by  the  magnetic  field 
than  that  on  the  cathode  side :    the  general   effect   of  this  will 
be   much   the   same  as  if  the   current  were  discontinuous,   and 
this,  as  we  have  seen  (see  p.  473),  corresponds  to  the  behaviour 
of  the  striated  column  in  the  magnetic  field. 

275.  Effect  of  a  constriction  in  the  tube.    Goldstein  (see  p.  466) 
has  shown  that  on  the  anode  side  of  a  constriction  we  get  negative 
glow ;  this  is  what  we  should  expect  on  the  preceding  theory,  for 
the  electric  force  in  the  constriction  will  be  greater  than  in  the 
wider  parts  of  the  tube :  there  are  several  lines  of  reasoning  by 
which  we  may  show  that  this  must  be  the  case ;  in  the  first  place 
the  current  density  in  the  constriction  is  greater  than  in  the  rest 
of  the  tube ;  thus  if  there  are  in  the  constricted  part  the  same 
number  of  ions  per  cubic  centimetre  as  elsewhere,  the  velocity  of 
the  ions  must  be  greater ;  for  this  to  be  the  case  the  electric  force 
must  be  greater  also :  or  again,  if  the  density  of  the  ions  is  greater 
in  the  constriction  than  in  the  wide  parts  of  the  tube,  then  since 
the  ions  are  produced  by  the  electric  field  the  larger  number  of 
ions  will  involve  a  more  intense  electric  field.     Thus,  as  the  force 
in  the  constriction  is  greater  than  in  the  rest  of  the  tube  the 


277]  THROUGH   VACUUM   TUBES.  491 

corpuscles  which  emerge  from  the  constriction  on  the  anode  side 
will  in  the  constriction  have  acquired  a  large  amount  of  kinetic 
energy,  and  will  therefore,  like  the  corpuscles  in  the  negative  glow, 
produce  great  ionisation  with  its  attendant  luminosity. 

276.  Effect   of  pressure   upon   the  electric  force.     We  shall 
consider  the  case  of  a  continuous  positive  column :  in  this  case 
the  reasoning  given  in  Art.  193  applies,  where  it  is  shown  that  if 
X  is  the  mean  free  path  of  a  corpuscle  and  X  the  electric  force, 
then   X\  is  constant ;  in  an  unlimited  gas  X  is  inversely  pro- 
portional to  the  pressure ;  hence  in  this  case  we  should  have  X 
proportional  to  the  pressure.     In  the  case  of  a  gas  contained  in  a 
tube   the  mean  free  path  will   be   somewhat  diminished  by  the 
restraint  imposed  by  the  tube ;  this  diminution  will  be  specially 
marked  when  the  pressure  of  the  gas  is  low  and  the  tube  narrow, 
If  X'  is  the  mean  free  path  of  the  corpuscle  in  the  tube  and  X  the 
free  path  in  an  unlimited  gas  at  the  same  pressure,  then  since  A/  is 
less  than  X,  X,  the  electric  force  in  the  tube,  will  be  greater  than 
that  in  the  free  gas.     This  agrees  with  experience,  as  we  find  the 
potential   gradient   greater   in  small  tubes  than   in   large   ones. 
Without  calculating  the  expression   for   the   mean  free  path  by 
a  rigorous  method  we  can  easily  in  a  general  way  see  how  the 
tube  will  affect  the  potential  gradient.     For  if  d  is  the  diameter 
of  the  tube,  then  when  d  is  large  compared  with  X,  X'  is  very 
approximately  equal  to  X ;  while  when  d  is  small  compared  with 
X,  X'  is  comparable  with  d ;  this  condition  will  be  satisfied  if 

I      a     I 
\     d     \' 

where  a  is  a  constant.     Since  X\'  is  constant,  we  have  X  pro- 
portional to  — ,  or  since  1/X  is  proportional  to  p  the  pressure,  we 
Xx 

have  X  =  A  +  Bp,  where  A  and  B  are  constants. 

277.  We  have  hitherto  supposed  that  the  ionisation  in  the 
discharge  tube  was  entirely  due  to  the  collisions  of  the  ions  with 
the  molecules  of  the  gas:    there  is,   however,  another  source  of 
ionisation.      E.   Wiedemann*   discovered   that  an    electric  spark 
emits  something  which  is  propagated  in  straight  lines,  is  stopped 

*  E.  Wiedemann,  Zeitschr.  /.  Electrochemie,  p.  159,  1895. 


492  DISCHARGE   THROUGH   VACUUM   TUBES.  [278 

by  all  solids  and  liquids,  and  which  possesses  the  power  of 
exciting  thermoluminescence  (see  p.  496)  in  suitable  bodies; 
he  called  this  radiation  from  the  spark  '  Entladungstrahlen.' 
Hoffmann*,  who  subsequently  investigated  this  question,  showed 
that  'Entladungstrahlen'  are  emitted  by  discharges  through 
vacuum  tubes  as  well  as  by  sparks,  and  that  this  radiation  is 
not  deflected  by  a  magnet ;  he  found  that  the  radiation  is 
absorbed  by  carbonic  acid  gas  to  a  much  greater  extent  than 
by  oxygen.  The  writer  f  showed  that  these  'Entladungstrahlen' 
possess  the  power  of  ionising  the  gas  through  which  they  pass, 
so  that  a  part,  though  often  only  a  small  part,  of  the  ionisation  in 
the  tube  is  due  to  these  rays.  The  rays  are  given  out  by  the 
luminous  parts  of  the  discharge,  i.e.  by  the  luminous  positive 
column  and  especially  by  the  luminous  parts  of  the  discharge 
near  the  cathode  ;  they  are  not,  however,  given  out  by  the  Faraday 
dark  space.  As  these  rays  help  to  ionise  the  gas  the  whole  of  the 
ionisation  has  not  to  be  done  by  the  collisions ;  so  that  the  strength 
of  the  field  required  to  produce  discharge  will  be  a  little  less 
than  that  calculated  on  the  collision  hypothesis ;  the  difference 
will  increase  with  the  strength  of  the  current,  so  that  the 
Entladungstrahlen  would  tend  to  make  the  potential  .gradients 
in  the  tube  diminish  as  the  strength  of  the  current  through  the 
tube  increases. 

278.  We  shall  see  that  when  the  motion  of  a  charged  ion  is 
accelerated  the  ion  emits  radiation  analogous  to  Rontgen  rays, 
the  energy  emitted  per  unit  time  being  e*f*l%V,  where  e  is  the 
charge  on  the  ion,  f  its  acceleration,  and  V  the  velocity  of  light. 
As  the  ions  carrying  the  current  in  the  discharge  tube  are  con- 
tinually being  accelerated  by  the  electric  force,  and  frequently, 
in  addition,  have  their  velocities  suddenly  altered  by  the  collisions 
they  make  with  the  molecules  of  the  gas,  during  which  time  their 
accelerations  are  very  great,  they  will  emit  radiation,  which  will  be 
most  intense  where  the  electric  force  is  greatest ;  this  radiation  is, 
I  think,  Wiedemann's  Entladungstrahlen. 

*  Hoffmann,  Wied.  Ann.  Ix.  p.  269,  1897. 

t  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.  x.  p.  74,  1899. 


CHAPTER  XVII. 

CATHODE  RAYS. 

279.     So  many  observations  have  been  made  on  these  rays,  - 
and  such  important  conclusions  drawn  from  them,  that  it  is  con- 
venient to  devote  a  separate  chapter  to  their  consideration. 

The  cathode  'rays  were  discovered  by  Plticker*  in  1859  ;  he 
observed  on  the  glass  of  a  highly  exhausted  tube  in  the  neighbour- 
hood of  the  cathode  a  bright  phosphorescence  of  a  greenish-yellow 
colour.  He  found  that  these  patches  of  phosphorescence  changed 
their  position  when  a  magnet  was  brought  near  to  them,  but 
that  their  deflection  was  not  of  the  same  nature  as  that  of  the  rest 
of  the  discharge  which  we  have  seen  he  had  carefully  studied. 
Plucker  ascribed  the  phosphorescence  to  currents  of  electricity 
which  went  from  the  cathode  to  the  walls  of  the  tube  and  then 
retraced,  for  some  reason  or  another,  their  steps. 

The  subject  was  next  taken  up  by  Pliicker's  pupil  Hittorf*f% 
to  whom  we  owe  the  discovery  that  a  solid  body  placed  between 
a  pointed  cathode  and  the  walls  of  the  tube  casts  a  well-defined 
shadow,  and  the  shape^f  the  shadow  only  depending  upon  that  of 
the  body,  and  not  upon  whether  the  latter  be  opaque  or  trans- 
parent, an  insulator  or  a  conductor.  This  observation  was  con- 
firmed and  extended  by  Goldstein  J,  who  found  that  a  well-marked, 
though  not  a  very  sharply  defined  shadow  was  cast  by  a  small 
body  near  the  cathode,  whose  area  was  much  greater  than  that  of 
the  body:  this  was  a  very  important  observation,  for  it  showed 
that  the  rays  producing  the  phosphorescence  came  in  a  definite 
direction  from  the  cathode.  If  the  cathode  were  replaced  by  a 

*  Pliicker,  Pogg.  Ann.  107,  p.  77,  1859;  116,  p.  45,  1862. 
f  Hittorf,  Pogg.  Ann.  136,  p.  8,  1869. 
J  Goldstein,  Berl.  Monat.  p.  284,  1876. 


494  CATHODE   RAYS.  [280 

luminous  disc  of  the  same  size  no  shadow  would  be  cast  by  a 
small  object  placed  near  it,  for  though  the  object  might  intercept 
the  rays  which  came  normally  from  the  disc,  yet  enough  light 
would  be  given  out  sideways  by  other  parts  of  the  disc  to  prevent 
the  shadow  being  well  marked.  Goldstein,  who  introduced  the 
term  '  Kathodenstrahlen '  for  these  rays,  regarded  them  as  waves 
in  the  ether,  a  view  which  received  much  support  in  Germany. 
A  very  different  opinion  as  to  the  origin  of  the  rays  was  expressed 
by  Varley*,  and  later  by  Crookesf,  who  advanced  many  and 
weighty  arguments  in  support  of  the  view  that  the  cathode  rays 
were  electrified  particles  shot  out  from  the  cathode  at  right  angles 
to  its  surface  with  great  velocity,  causing  phosphorescence  and 
heat  by  their  impact  with  the  walls  of  the  tube,  and 'suffering  a 
deflection  when  exposed  to  a  magnetic  field  by  virtue  of  the 
charge  they  carried.  The  particles  in  this  theory  were  supposed 
to  be  of  the  dimensions  of  ordinary  molecules ;  the  discovery 
made  by  Hertzj  that  the  cathode  rays  could  penetrate  thin  gold- 
leaf  or  aluminium  was  difficult  to  reconcile  writh  this  view  of  the 
cathode  rays;  although  it  was  possible  that  the  metal  when  exposed 
to  a  torrent  of  negatively  electrified  particles  acted  itself  like  a 
cathode  and  produced  phosphorescence  on  the  glass  behind. 
The  measurements  described  in  Chapter  V.  of  the  mass  of  the 
particles  carrying  the  charge  show  that  though  the  cathode  rays 
do  consist  of  negatively  electrified  particles,  the  particles  are  not 
of  the  dimensions  of  even  the  smallest  molecules,  having  a  mass 
only  about  one-thousandth  part  of  .that  of  a  molecule  of  hydrogen. 
We  shall  now  proceed  to  describe  the  properties  of  the  cathode 
rays  in  detail,  beginning  with  that  which  led  to  their  discovery, 
viz.  the  phosphorescence  they  produce  when  they  fall  on  solids. 

i 

280.  The  colour  of  the  phosphorescent  light  they  produce 
when  they  fall  on  glass  depends  upon  the  nature  of  the  glass; 
thus  with  soda  glass  the  light  is  yellowish-green,  with  lead  glass  it 
is  blue.  A  very  large  number  of  bodies  become  phosphorescent 
when  exposed  to  these  rays;  indeed,  this  phosphorescence  often 
affords  a  convenient  means  for  detecting  the  rays :  as  phosphor- 
escence is  very  easily  excited  in  potassium  platino-cyanide  a 

*  Varley,  Proc.  Roy.  Soc.  xix.  p.  236,  1871. 

t  Crookes,  Phil.  Trans.  Pt.  i.  1879,  p.  135 ;  Pt.  n.  1879,  p.  641. 

£  Hertz,  Wied.  Ann.  xlv.  p.  28,  1892. 


281]  CATHODE  RAYS.  495 

screen  of  this  substance  is  often  used  to  detect  the  rays.  The 
spectrum  of  the  light  given  out  by  bodies  when  phosphorescing 
under  bombardment  by  these  rays  is  generally  a  continuous  one. 
Sir  William  Crookes*  has  shown  that  when  the  cathode  rays  fall 
on  some  of  the  rare  earths,  such  as  yttrium,  the  substance  gives 
out  a  spectrum  with  bright  bands ;  he  has  founded  on  this  obser- 
vation a  spectroscopic  method  which  is  of  the  greatest  importance 
in  the  study  of  the  rare  earths f)  These  earths  are  luminous 
when  raised  to  a  high  temperature  as  in  the  mantles  of  Welsbach 
burners ;  there  is,  however,  a  marked  difference  between  the 
incandescence  produced  in  this  way  and  that  produced  by  cathode 
•rays ;  thus  in  the  Welsbach  burner  the  addition  of  1  per  cent,  of 
ceria  to  thoria  increases  the  luminosity*  elevenfold  as  compared 
with  that  of  pure  thoria.  Campbell  S  win  ton  J  has  shown,  however, 
that  it  produces  no  appreciable  change  in  the  luminosity  under 
cathode  rays :  again,  in  the  flame  pure  ceria  gives  about  as  much 
light  as  pure  thoria,  while  under  cathode  rays  pure  thoria  gives 
a  brilliant  light,  and  pure  ceria  practically  no  light  at  all. 

281.  The  impact  of  the  cathode  rays  produces  in  some  cases 
very  definite  chemical  changes ;  thus  Goldstein  §  has  shown  that 
the  haloid  salts  of  the  alkali  metals  change  colour  when  exposed 
to  the  rays ;  thus  for  example,  crystals  of  rock-salt  acquire  under 
the  rays  a  beautiful  violet  tint ;  this  tint  is  not  permanent, 
though  under  certain  circumstances  the  rate  of  decay  is  exceed- 
ingly slow :  thus  there  are  at  the  Cavendish  Laboratory  some  of 
these  crystals,  which,  corked  up  in  a  test-tube  but  not  kept  in  the 
dark,  have  retained  a  strong  coloration  for  more  than  five  years: 
exposure  to  moisture  causes  the  colour  to  fade  away  rapidly. 
Lithium  chloride  is  especially  easily  coloured ;  if  a  beam  of  cathode 
rays  is  slowly  moved  over  the  salt  by  a  magnet  the  path  of  the 
beam  traces  out  a  coloured  band  over  the  surface  of  the  salt. 
Similar  changes  in  colour  can  be  produced  by  chemical  means ; 
thus  if  sodium  chloride  is  heated  up  with  -sodium  vapour  it  gets 
coloured  in  much  the  same  way  as  if  it  were  exposed  to  cathode 
rays ;  the  coloured  salt  is  also  produced  at  the  cathode  in  the 

*  Crookes,  Phil.  Trans.  Pt.  n.  1879,  p.  661. 

t  Ibid.  Pt.  in.  1883;  Pt.  n.  1885. 

J  Campbell  Swinton,  Proc.  Roy.  Soc.  Ixv.  p.  115,  1900. 

§  Goldstein,  Wied.  Ann.  liv.  p.  371,  1899^ y 


496  CATHODE   RAYS.  [282 

electrolysis  of  haloid  salts.  The  coloured  salt  also  occurs  native. 
According  to  E.  Wiedemann  and  Schmidt*  the  coloration  is 
due  to  the  formation  of  a  sub-chloride.  Elster  and  Geitelf 
discovered  that  these  coloured  salts  are  very  photo-electric,  dis- 
charging negative  electricity  when  exposed  to  light ;  behaving,  in 
fact,  as  if  they  contained  traces  of  the  free  metal.  The  glass  of  a 
vacuum  tube  also  acquires  a  violet  tint  after  long  use. 

282.  The  power  of  the  glass  to  phosphoresce  is  deadened  by 
long  exposure  to  cathode  rays  :  this  is  very  beautifully  shown  in 
an  experiment  made  by  Crookes  J ;    the  shadow  of  a  mica  cross 
was  thrown  upon  the  walls  of  the  tube ;  after  the  discharge  had 
been  running  for  some  time  the  cross  was  shaken  down  or  a  new 
cathode  in  a  different  part  of  the  tube  was  used ;  the  pattern  of 
the  cross  could  still  be  traced  on  the  glass,  but  it  was  now  brighter 
than  the   rest   of  the   glass  instead    of   darker  as   before.     The 
portions  outside  the  original  pattern  got  tired  by  the  bombard- 
ment, and  so  in  the  second  part  of  the  experiment  phosphoresced 
less  brightly  than  the  portions  inside  the  original  shadow  which 
were  now  bombarded  for  the  first  time.     Crookes  found  that  this 
change  in  the  phosphorescence  of  the  glass  persisted  even  after 
the  glass  had  been  fused  and  again  allowed  to  cool. 

283.  Villard§  found  that  cathode  rays  exert  a  reducing  action  ; 
thus  if  they  fall  upon  an  oxidised  copper  plate,  the  part  exposed  to 
the  rays  becomes  bright.     In  considering  the  chemical  effects  pro- 
duced by  the  rays  we  ought  not  to  forget  that  the  incidence  of 
the  rays  is  often  accompanied  by  a  great  increase  in  temperature, 
and  that  some  of  the  chemical  changes  may  be  secondary  effects 
due  to    the    heat   produced  by   the  rays.     Platinum   after   long 
exposure  to  the  rays  gets  covered  with  platinum  black. 

284.  Tliermoluminescence.      In    some    cases,  even   when    no 
visible  coloration  is  produced,  the  behaviour  of  the  body  after 
exposure  to  the  rays  shows  that  it  has  been  changed.     A  very 
striking  instance  is  the  case  called  by  E.  Wiedemann ||  'Tliermo- 
luminescence.'     Some   bodies,    after    exposure   to   cathode    rays, 

*  Wiederaann  and  Schmidt,  Wied.  Ann.  liv.  p.  262,  1895 ;  Ixiv.  p.  78,  1898. 

t  Elster  and  Geitel,  Wied.  Ann.  lix.  p.  487,  1896. 

t  Crookes,  Phil.  Trans.  Pt.  n.  p.  645.  1879. 

§  Villard,  Journal  de  Physique,  3me  Serie,  t.  viii.  p.  140,  1899. 

II  E.  Wiedemanu  and  Schmidt,  Wied.  Ann.  liv.  p.  604,  1895. 


284] 


CATHODE   RAYS. 


497 


are  found  to  possess  for  some  time  the  power  of  becoming 
luminous  when  their  temperature  is  raised  to  a  point  far  below 
that  at  which  they  become  luminous  when  in  their  normal  state ; 
they  retain  this  property  for  weeks,  and  even  months,  after  ex- 
posure to  the  rays.  The  substances  in  which  this  property  is 
most  highly  developed  belong  to  the  class  of  bodies  called  by 
Van  't  Hoff*  solid  solutions;  these  are  formed  by  precipitating 
simultaneously  from  a  solution  two  salts,  one  greatly  in  excess 
of  the  other.  The  influence  of  a  slight  trace  of  a  second  substance 


Substance 

Cathode 
phosphorescence 

After-glow 

Thermo- 
luminescence 

CaS04 

faint  yellowish 

none 

none 

CaS04-f^MnS04  .    ... 

red 

intense  green 

strong  green 

intense  green 

SrS04  

none 

SrS04  +  #MnS04 

bright  red 

perceptible 

perceptible 

BaS04 

faint  dark  violet 

»BaS04  +  x  MnS04 

dark  blue 

faint 

very  faint 

MgSCX.. 

red 

perceptible 

feeble 

MgS04  +  l°/0MnS04... 
ZnSO,.. 

intense  dark  red 
bright,  white 

persistent 
persistent 

intense  red 
white 

ZnS04+l%MnS04... 
Na2S04    

intense  red 
bluish 

very  persistent 
faint 

very  strong  red 
bright 

Na2S04  +  0'5%MnS04 
CdS04 

intense  brown- 
ish yellow 
yellow 

strong 
persistent 

bright  yellow 
bright  yellow 

CdS04  +  l%MnS04... 
CaFl2  

intense  yellow 
faint  bluish 

very  persistent 
very  faint 

intense  yellow 
faint 

CaFl2  +  #MnFl2  

intense  green 

persistent 

intense  green 

on  the  phosphorescence  produced  while  the  rays  are  playing  on 
the  substance ;  the  after-glow,  which  lingers  for  a  time  after  the 
rays  are  stopped;  and  the  thermoluminescence  is  shown  by  the 

*  Van  't  Hoff,  Zeitschr.  /.  physik.  Chem.  v.  p.  322,  1890. 
T.  G.  32 


498  CATHODE  RAYS.  [285 

preceding  table,  due  to  E.  Wiedemann  and  Schmidt*.  By  the 
symbol  CaSO4  +  #MnSO4  is  meant  a  'solid  solution'  of  a  trace 
of  MnS04  in  a  matrix  of  CaS04. 

The  '  Entladungstrahlen '  (see  p.  491)  also  give  rise  to  thermo- 
luminescence,  as  Wiedemann  found  that  any  of  the  preceding 
substances  showed  thermoluminosity  if  sparks  were  produced 
close  to  them. 

285.  We   may  compare  the  after-glow  observed  with   these 
solids  with  that  which   is  observed  when   the  electric  discharge 
passes  through  certain  gases  which  are  found  to  remain  luminous 
for  a  considerable  time  after  the  discharge   has  passed  through 
them.     It  is  not  necessary  that  the  discharge  should  consist  of 
cathode  rays;  most  kinds  of  discharges   will  produce  this  after- 
glow if  the  pressure  is  suitable ;   it  is  exceptionally  conspicuous 
in  electrodeless   discharges   and   is   especially  well  developed  in 
oxygen  and  cyanogen,  gases  which  polymerise  with  great  ease. 
I  think  there  are  strong  reasons  for  believing  that  the  after-glow 
is  very  closely  connected  with  the  power  some  gases  possess  of 
polymerising  and  forming  complex  molecules;  and  that  the  gradual 
return  of  the  gas  from  its  polymerised  to  its  normal  form  is  accom- 
panied by  the  emission  of  light. 

286.  Like  the  thermoluminescence  of  solids,  the  after-glow  in 
gases  seems  to  be  increased  by  the  presence  of  small  quantities  of 
impurities;  thus   it  is  brighter  in  oxygen  with  a  little  nitrogen 
than  in  pure  oxygen.      Newallf  discovered    a  very  remarkable 
effect  connected  with  the  after-glow  in  oxygen  ;  he  found  that  with 
the  electrodeless  discharge  the  after-glow  was  only  developed  when 
the  pressure  was  between  the  limits  '6  mm.  and  "01  mm.     If  the 
discharge  is  sent  through  the  gas  at  a  pressure  not  between  these 
limits,  there  is  no  glow,  but  if  after  the  discharge  has  ceased  the 
pressure  is  altered  so  as  to  come  within  the  limits  the  gas  at  once 
begins  to  glow,  suggesting  that  the  polymerised  form  is  stable,  i>e. 
does  not  go  back  into  the  normal  form  except  between  the  limits 
•C  mm.  and  '01  mm.     It  may  be  mentioned  that  this  is  the  region 
of  pressure  in  which  some  observers,  though  not  all,  have  observed 
large  departures  from  Boyle's  law. 

*  Wiedemann  and  Schmidt,  Wied.  Ann.  Ivi.  p.  201,  1895. 
t  Newall,  Proc.  Camb.  Phil.  Soc.  ix.  p.  295,  1897. 


288]  CATHODE   RAYS.  499 

In  the  case  of  phosphorescent  solids  and  liquids  we  may  regard 
the  phosphorescence  as  arising  in  the  following  way.  The  cathode 
rays  or  Entladungstrahlen  will  ionise  the  substance,  causing 
complex  substances  to  be  formed  which  phosphoresce  as  they 
break  up  into  their  original  constituents ;  some  of  these  complex 
molecules  are  unstable  at  the  temperature  of  the  room  and  at 
once  begin  to  decompose,  giving  rise  to  the  after  phosphorescence 
of  the  glass,  etc. ;  others  are  stable  at  ordinary  temperatures,  but 
are  unstable  and  decompose  at  high  temperatures ;  these  produce 
thermoluminescence. 

287.  McClennan*  has  shown  that  some  salts,  especially  the 
sulphates  of  potassium,  barium,  strontium  and  calcium,  after  ex- 
posure to  cathode  rays,  or  to  the  radiation  from  a  spark,  possess 
the   power   of  discharging  a  positively   electrified   body   placed 
near   them   in   a   gas   at   low   pressure,  behaving   in   fact   as   if 
they  were  photo-electric  bodies  exposed  to  the  action  of  ultra- 
violet light,  i.e.  they  emit  slowly  moving  negatively  electrified 
corpuscles.     McClennan   made   experiments  to   show  that  there 
was  no  emission  of  ultra-violet  light  from  the  heated  salts.     There 
does  not  seem  to  be  any  connection  between  the  powers  of  salts  to 
produce  the  effect  discovered  by  McClennan  and  their  power  of 
producing  thermoluminescence:    as  McClennan  found  that  many 
salts  which  glowed  strongly  when  heated  did  not  give  his  effect, 
which  was  given  by  some  salts  which  hardly  showed  any  thermo- 
luminescence. 

288.  Thermal   effects  produced   by  the  rays.      The  cathode 
rays  heat  bodies  on  which  they  fall,  and  if  the  rays  are  concen- 
trated by  using  a  portion  of  a  hollow  cylinder  or  spherical  shell 
as  a  cathode,  platinum  may  be  raised  to  incandescence,  thin  pieces 
of  glass  fused,  and  the  surface  of  a  diamond  charred. 

Measurements  of  the  amount  of  heat  developed  by  the  rays 
have  been  made  by  E.  Wiedemann  and  Ebertf,  E.  Wiedemann  J, 
and  Ewers  §.  A  simple  example  will  give  some  idea  of  the 
amount  of  energy  carried  by  the  rays.  If  n  is  the  number 

*  M'Clennan,  Phil  Mag.  vi.  3,  p.  195,  1902. 

t  Wiedemann  and  Ebert,  Sitz.  der  phys.  med.  Soc.  Erlangen,  Dec.  1891. 

I  E.  Wiedemann,  Wied.  Ann.  Ixvi.  p.  61,  1898. 

§  Ewers,  Wied.  Ann.  Ixix.  p.  167,  1899. 

32—2 


500  CATHODE   RAYS.  [289 

of  corpuscles  striking  a  body  in  unit  time,  m  the  mass  of  a 
corpuscle,  and  v  its  velocity,  then  E  the  energy  possessed  by  the 
corpuscles  striking  the  body  in  unit  time  is  ^nmv* ';  if  all  the 
corpuscles  coming  from  the  cathode  are  caught  by  the  body  and 
e  is  the  charge  on  a  corpuscle,  then  ne  =  I,  the  current  carried 

by  the  corpuscles;  thus  E=^I  —  v*:  now  10~5  amperes  is  not  an 

exceptionally  high  value  for  /,  and  if  v  -  o  x  109  cm./sec.  we  get, 
since  m/e=W~7,  E—  12'5  x  105;  thus  the  energy  possessed  by 
the  corpuscles  striking  the  body  per  minute  would  be  nearly 
2  calories. 

289.  The  impact  of  the  corpuscles  does  more  than  heat  the 
body,  it  makes  it  phosphoresce,  it  produces  Rontgen  rays,  and 
causes  the  body  to  emit  cathode  rays.  Interesting  information  is 
afforded  by  measuring  the  heat  produced  by  the  cathode  rays, 
and  also  the  charge  of  electricity  brought  to  the  body  by  the 
rays;  such  measurements  have  been  made  by  the  author*,  and 
later  in  greater  detail  by  Cadyf.  Cady's  method  was  to  measure 
(1)  the  heat  produced  in  a  bolometer  strip  against  which  the  rays 
struck,  and  (2)  the  negative  charge  acquired  by  the  bolometer 
per  second ;  the  latter,  it  is  important  to  notice,  need  not  be 
the  same  as  the  charge  carried  by  the  corpuscles  striking  the 
body  in  one  second,  for  some  of  the  corpuscles  may  rebound  from 
the  body  without  giving  up  a  charge,  or  the  impact  of  the  rays 
may  cause  the  body  to  give  out  cathode  rays,  carrying  from  it 
a  negative  charge,  or  positively  electrified  atoms,  giving  to  it  an 
additional  negative  charge ;  thus  if  /  is  the  charge  carried  by  the 
corpuscles,  i  that  acquired  by  the  bolometer  per  second,  then  /  is 
not  necessarily  the  same  as  i.  If  V  is  the  potential  difference 
between  the  electrodes  in  the  tube,  then  the  energy  carried  by 
the  corpuscles  is  VI.  Cady  measured  the  ratio  of  Vi  to  Q  the 
mechanical  equivalent  of  the  heat  developed  in  unit  time ;  he 
found  that  this  ratio  depends  greatly  upon  the  value  of  i ;  as  long 
as  i  is  large  it  is  greater  than  unity,  diminishing  as  i  diminishes ; 
when  i  gets  very  small  (less  than  10~7  amperes),  the  ratio  becomes 
constant  and  equal  to  '83 ;  as  the  ratio  is  less  than  unity  it  follows 
that  there  is  an  emission  of  negative  electricity  from  the  bolometer, 

*  J.  J.  Thomson,  Phil.  Mag.  v.  44,  p.  293,  1893. 
t  Cady,  Drude's  Ann.  i.  p.  678,  1900. 


290]  CATHODE   RAYS.  501 

either  by  the  reflection  of  the  cathode  rays,  or  by  the  emission  of 
secondary  cathode  rays  from  its  surface.  We  have  seen  that  the 
measurement  of  i  and  V  does  not  give  the  energy  reaching  the 
surface  through  the  cathode  rays ;  a  slight  modification  of  the  ex- 
periment would,  however,  give  the  data  by  which  this  energy  could 
be  determined;  all  that  is  necessary  would  be  to  surround  the 
bolometer  by  an  insulated  Faraday  cylinder,  into  which  the  rays 
were  admitted  through  a  small  opening,  and  then  to  measure  the 
charge  received  by  this  cylinder  in  unit  time. 

E.  Wiedemann*  has  shown  that  the  energy  spent  in  pro- 
ducing phosphorescence  is  but  a  small  fraction  of  the  incident 
energy. 

290.  Mechanical  effects  produced  by  the  rays.  A  secondary 
result  of  the  thermal  effects  produced  by  the  rays  are  the  very 
interesting  mechanical  effects  which  have  been  especially  studied 
by  Crookes  I"  and  Puluzj.  A  typical  example  of  these  is  afforded 
by  the  well-known  experiment  due  to  Crookes  represented  in 
Fig.  163,  where  the  axle  of  a  very  light  mill  with  a  series  of  vanes 


Fig.  163. 

is  mounted  on  glass  rails,  in  a  vacuum  tube ;  when  the  discharge 
passes  through  the  tube  the  cathode  rays  strike  against  the  upper 
vanes  and  the  wheel  rotates  and  travels  from  the  negative  to  the 
positive  end  of  the  tube. 

A  simple  calculation  will  show  that  we  cannot  ascribe  the 
rotation  to  the  momentum  communicated  to  the  vanes  by  the 
impact  of  the  corpuscles  against  them ;  for,  take  the  case  when 
the  rays  are  so  powerful  that  they  carry  the  very  large  current  of 
10~5  amperes,  and  that  they  move  with  the  very  high  velocity  of 
1010  cm./sec. :  if  N  is  the  number  of  corpuscles  striking  a  surface 
in  unit  time,  m  the  mass  of  the  corpuscles ;  then  supposing  the 

*  E.  Wiedemann,  Wied.  Aim.  Ixvi.  p.  61,  1898. 

t  Crookes,  Phil.  Trans.  1879,  pt.  i.  p.  152. 

£  Puluz,  Radiant  Electrode  Matter.   Physical  Society's  Bepriut  of  Memoirs,  p.  275. 


502  CATHODE   RAYS.  [291 

corpuscles  to  rebound  from  the  surface  with  a  velocity  equal  to 
that  with  which  they  impinge  against  it,  the  momentum  commu- 
nicated to  the  surface  in  unit  time  is  2NmWw ;  if  e  is  the  charge 
carried  by  a  corpuscle,  then  Ne  is  the  current  carried  by  the  rays, 
in  our  case  10"6  in  absolute  measure ;  hence  the  momentum 

7?? 

communicated  to  the  surface  per  second  is  equal  to  2  — 104  dynes, 

& 

or  as  m/e  =  10~7  to  2  x  10~3  dynes :  this  is  equivalent  to  a  differ- 
ence of  pressure  on  the  two  sides  of  a  vane  1  sq.  cm.  in  area  of  one- 
five-hundred-millionth  part  of  an  atmosphere  ;  an  effect  altogether 
too  small  to  explain  the  movement  of  a  body  such  as  that  repre- 
sented in  Fig.  163.  This  movement  is  probably  due  to  an 
effect  similar  to  that  observed  in  a  radiometer,  as  the  impact 
of  the  cathode  rays,  will  make  one  side  of  the  vanes  much 
hotter  than  the  other.  Starke*  has  shown  that  when  the  vanes 
are  arranged  so  that  the  radiometer  effect  is  eliminated,  the 
mechanical  effect  is  exceedingly  small — in  his  experiments,  where 
the  current  carfied  by  the  cathode  rays  was  10~7  amperes  and  the 
potential  difference  10,000  volts — certainly  less  than  10~4  dynes. 

291.  Electric  charge  carried  by  the  cathode  rays.  The  fact 
that  the  cathode  rays  carry  a  negative  charge  of  electricity  was 
proved  in  a  very  direct  way  by  Perrin-f-.  Fig.  164  represents 
a  modification  of  his  experiment.  The  rays  start  from  the 


Fig.  164. 

cathode  A  and  pass  through  a  slit  in  a  brass  rod  B,  which  fits 
lightly  into  the  neck  of  the  tube ;  this  rod  is  connected  with  the 

*  Starke,  Drude's  Ann.  iii.  p.  101,  1900. 

t  Perrin,  Comptes  Rendus,  cxxi.  p.  1130,  1895. 


292]  CATHODE   RAYS.  503 

earth  and  used  as  an  anode ;  the  rays  after  passing  through  the 
slit  enter  the  spherical  vessel  C.  In  this  vessel  there  are  two 
coaxial  metal  cylinders,  the  outer  one  D  connected  with  the 
earth,  the  inner  one  E  carefully  insulated  and  connected  with  an 
electrometer.  The  cylinders  are  placed  so  as  to  be  out  of  the 
direct  line  of  fire  of  the  rays.  When  the  discharge  passed 
through  the  tube  and  the  cathode  rays  passed  horizontally  through 
the  vessel  C,  the  inner  cylinder  E  received  a  small,  but  only  small, 
negative  charge.  The  cathode  rays  /were  then  deflected  by  a 
magnet;  their  path  could  be  inferred  from  the  position  of  the 
phosphorescent  patch  on  the  walls  of  (7;  when  the  deflection  was 
increased,  so  that  the  position  of  the  path  showed  that  the  rays 
had  fallen  on  fhe  opening  of  the  cylinders,  there  was  a  very  great 
increase  in  the  negative  charge  received  by  E ;  when  the  rays  had 
been  so  much  deflected  that  the  phosphorescent  patch  fell  below 
the  slit  the  negative  charge  in  the  cylinder  E  again  disappeared. 
This  experiment  shows  that  the  rays  carry  a  negative  charge, 
as  it  proves  that  the  negative  electrification  follows  exactly  the 
same  course  as  the  rays  producing  the  phosphorescence  on  the 
glass. 

This  experiment  also  shows  that  the  cathode  rays  make  the 
gas  through  which  they  j3ass__a  conductor  of  electricity ;  for  if  in 
the  experiment  the  discharge  is  kept  continuously  passing  through 
the  tube  and  the  cathode  rays  deflected  until  they  pass  into  the 
cylinder,  the  negative  charge  on  the  cylinder  will  rise  to  a  certain 
value,  beyond  which  it  will  not  increase  however  long  the  discharge 
may  be  kept  running ;  this  shows  that  the  gas  around  the  cylinder 
is  a  conductor,  and  the  steady  state  of  the  cylinder  is  reached  when 
it  loses  as  much  electricity  by  conduction  through  the  gas  as  it 
gains  from  the  cathode  rays.  The  same  thing  is  shown  when  the 
cylinder  is  given  a  negative  charge  before  the  discharge  through 
the  gas  begins :  if  this  charge  is  less  than  a  certain  value  the 
cathode  rays  will  increase  the  charge  ;  if  however  it  is  greater  than 
this  value,  the  cathode  rays  will  diminish  the  charge  until  it 
falls  to  this  critical  value. 

292.  Reflection  of  cathode  rays.  When  cathode  rays  strike 
the  surface  of  either  a  conductor  or  an  insulator  cathode  rays 
start  from  the  surface  in  all  directions ;  this  phenomenon  is  called 
the  diffuse  reflection  of  the  cathode  rays:  we  must  be  careful 


504  CATHODE   RAYS.  [293 

however  to  remember  that  reflection  is  used  in  a  different  sense 
from  that  which  is  usual  in  optics,  where  for  example  we  should 
not  speak  of  the  phosphorescent  light  given  out  by  such  a  sub- 
stance as  quinine  when  struck  by  ultra-violet  light  as  reflected 
rays;  in  the  case  of  the  cathode  rays  all  the  cathode  rays  pro-y 
ceeding  from  a  surface  struck  by  cathode  rays  are  called  reflected 
rays.  The  existence  of  such  rays  is  easily  shown  by  an  experi- 
ment due  to  Goldstein*.  The  cathode  rays  from  the  cathode  G 


Fig.   165. 

fall  on  the  plate  A  which  can  be  rotated  by  a  handle  passing 
through  a  stuffing-box.  The  half  of  the  tube  AB  on  the  illu- 
minated side  of  A  becomes  phosphorescent  from  the  cathode 
rays  diffusely  reflected  from  A.  The  reflection  occurs  even  when 
the  plate  does  not  itself  become  phosphorescent  under  cathode 
rays. 

293.  Measurements  of  the  amount  of  '  reflection '  experienced 
by  cathode  rays  when  incident  upon  different  substances  and  at 
different  angles  of  incidence  have  been  made  by  Campbell 
Swintonf,  by  StarkeJ,  and  by  Austin  and  Starke§.  Campbell 
S  win  ton's  experiments,  which  had  for  their  object  the  measure- 
ment of  the  variation  of  the  '  reflected '  rays  at  various  angles  of 
incidence  and  emergence,  were  arranged  as  represented  in  Fig.  1G6. 
C  is  the  cathode ;  A  the  reflecting  surface,  a  flat  piece  of  platinum 
which  could  be  rotated  about  its  axis ;  F  a  Faraday  cylinder  which 
receives  the  rays  emitted  by  the  surface ;  this  could  be  set  so  that 
the  opening  made  any  required  angle  with  the  direction  of  the 
incident  rays ;  the  charge  received  by  this  cylinder  was  taken  as 
the  measure  of  the  amount  of  reflection.  Campbell  Swinton 

*  Goldstein,  Wied.  Ann.  xv.  p.  254,  1882. 

+  Campbell  Swinton,  Proc.  Roy.  Soc.  Ixiv.  p.  377,  1899. 

£  Starke,  Wied.  Ann.  Ixvi.  p.  49,  1898 ;  Drude's  Ann.  iii.  p.  75,  1900. 

§  Austin  and  Starke,  Drude's  Ann.  ix.  p.  271,  1902. 


293] 


CATHODE   RAYS. 


505 


came  to  the  conclusion  that  although  the  'reflection'  was  very 
diffuse  there  was  appreciably  more  in  the  direction  in  which  the 
angle  of  emergence  was  equal  to  the  angle  of  incidence  than  in 


Fig.  166. 

any  other  direction ;  he  found  that  the  total  amount  of  emission 
was  slightly  greater  at  oblique  than  at  normal  incidence ;  he 
measured  also  the  charge  received  by  the  reflector  and  found 
that  though  with  normal  incidence  it  received  a  large  negative 
charge,  the  charge  diminished  as  the  incidence  became  more 
oblique,  vanished,  and  finally  with  very  oblique  incidence  became 
positive.  The  positive  charge  received  by  the  reflector  has  also 
been  observed  by  Austin  and  Starke  (I.e.). 

Starke  determined  the  proportion  between  the  incident  and 
receding  rays,  or  rather  the  ratio  of  the  negative  charge  acquired 
by  the  reflector  to  that  carried  by  the  receding  rays. 

The  principle  of  the  method  used  by  Starke  is  as  follows.  The 
cathode  rays  enter  through  a  hole  in  the  cylinder  and  strike  the 
reflector ;  the  cylinder  and  reflector  are  each  connected  to  earth 
through  high-resistance  galvanometers ;  when  the  rays  strike 
against  the  reflector  currents  pass  through  these  galvanometers ; 


506 


CATHODE   RAYS. 


[293 


let  i*!,  i2  be  the  currents  through  the  galvanometers  connected  with 
the  reflector  and  cylinder  respectively;  let  N  be  the  number  of 
corpuscles  striking  the  reflector  in  unit  time,  n  the  number  leaving 


B 


Fig.  167. 

it  in  the  same  time,  e  the  charge  on  a  corpuscle ;  then,  if  there  is 
no  ionisation  in  the  gas  of  the  cylinder,  no  escape  of  the  receding 
rays  through  the  hole,  and  no  diffusion  of  the  incident  rays  in  the 
cylinder  causing  some  of  the  incident  rays  to  strike  the  walls  of 
the  cylinder  instead  of  the  reflector,  we  have 

(N  —  n}  e  =  ii ;  ne  —  i2 ; 


or 


hence  if  we  measure  ^  and  iz  we  can  determine  the  value  of  n/N ; 
in  practice  some  corrections  are  necessary,  for  which  we  must 
refer  to  Starke's  paper  (/.c.);  the  value  of  n/N  depends  upon  the 
metal ;  the  following  are  Starke's  values  for  this  quantity : 


Metal 

Density 

njN 

Metal 

Density 

njN 

Pt  .. 

21-5 

•72 

Brass     .  .  . 

8-1 

•43 

Pb  

11-3 

•63 

Fe  

7-7 

•40 

Ag  

10-5 

•59 

Zn  

7-1 

•40 

Bi  .. 

9-9 

•58 

Al 

2-6 

•25 

Ni  

8-9 

•48 

Mg 

1-7 

•25 

Cu...     . 

8'5 

•45 

Thus  the  value  of  n/N  increases  with  the  density  of  the  metal ; 
the  numbers  given  above  are  roughly  proportional  to  the  square 
root  of  the  density ;  we  see  that  even  for  the  lightest  metals  the 
number  of  corpuscles  receding  from  the  surface  is  as  much  as 
one  quarter  of  the  number  of  those  approaching  it.  The  pre- 
ceding values  of  n/N  are  when  the  incidence  of  the  cathode  rays 
is  normal;  in  this  case  n/N  does  not  depend  upon  the  velocity  of 
the  incident  rays. 


295]  CATHODE   RAYS.  507 

294.  The  fact  observed  by  Campbell  Swinton  (I.  c.)  that  when 
the  incidence  is  very  oblique  the  reflector   acquires  a  positive 
instead  of  a  negative  charge,  has  been  carefully  studied  by  Starke 
and  Austin*,  who   have   measured   the   charge  received  by  the 
reflector  for  cathode  rays  incident  at  various  angles;   they  find 
that  the  angle  of  incidence  at  which  the  charge  received  by  the 
reflector  changes  from  —  to  +  depends  on  the  material  of  which 
the  reflector  is  made  and  the  velocity  of  the  rays.     With  denser 
reflectors  the  change  from  —  to  4-  takes  place  at  a  smaller  angle 
of  incidence  than  it  does  with  lighter  reflectors ;  and,  again,  the 
smaller  the  velocity  of  the   rays  the  smaller  the  critical  angle. 
The  amount  of  influence   exerted  by  the  nature  of  the  metal, 
and  the  velocity  of  the  rays,  may  be  illustrated  by  the  following 
numbers  due  to  Austin  and  Starke.     With  a  platinum  reflector, 
and   with    cathode   rays   produced   by  a  potential    difference    of 
9000  volts,  the  critical  angle  of  incidence  was  60° ;  with  a  copper 
reflector,  and  a  potential  difference  of  8700  volts,  the  critical  angle 
was  80°,  and  with  a  potential  difference  of  5000  volts,  70°. 

295.  Since,  in  some  cases,  the  reflector  receives  a  positive 
charge  from  the  impact  of  the  negatively  electrified  corpuscles, 
more  corpuscles  must  leave  the  surface  than  arrive  at  it ;  it  follows 
that  the  velocity  of  the  receding  corpuscles  must,  on  the  average, 
be  less  than  that  of  the  approaching  ones,  otherwise  the  energy 
emitted  by  the  reflector  would  be  greater  than  the  energy  re- 
ceived.    Measurements  of  the  velocity  of  the  '  reflected '  rays,  by 
means  of  the  deflection  they  experience  in  a  magnetic  field,  have 
been  made  by  Merritt  f,  Austin  and  Starke  (I.e.),  and  Gehrckej; 
both  Merritt  and  Austin  and  Starke  came  to  the  conclusion  that 
the  velocity  of  the  reflected  rays  was  much  the  same  as  that  of 
the   incident;   Gehrcke,    however,   by   a  very  ingenious   method 
showed  that  among  the  'reflected'  rays  there  were  a  large  number 
whose  velocities  were  considerably  less  than  that  of  the  incident 
rays.    Gehrcke's  method  is  represented  in  Fig.  168;  Kt  and  K2  are 
two  cathodes  connected  together  and  with  the  negative  pole  of 
an  electrical  machine;  the  rays  from  K^  went  straight  from  the 
cathode  on  to  a  fluorescent  screen  FF\  while  those  from  K2  fell  on 

*  Austin  and  Starke,  Drude's  Ann.,  ix.  p.  271,  1902. 
t  Merritt,  Physical  Review,  vii.  p.  217,  1898. 
J  Gehrcke,  Drude's  Ann.,  viii.  p.  81,  1902. 


508 


CATHODE  KAYS. 


[295 


a  magnesium  reflector,  the  '  reflected'  rays  from  which  fell  on  the 
same  screen.     J"a  and  «7~2  are  the  coils  for  producing  the  magnetic 


Fig.  168. 

field.     The  appearance  of  the  phosphorescence  on  the  screen  be- 
fore and  after  the  magnetic  field  was  started  is  shown  in  Fig.  169. 


LAHHHHH— 


Fig.  169. 


The  middle  patches  F,  F'  represent  the  phosphorescence  without 
a  magnetic  field  due  to  the  direct  and  reflected  rays  respectively; 
the  patches  above  and  below  these  represent  the  phosphorescence 
when  the  magnetic  field  was  on,  the  upper  and  lower  patches 
corresponding  to  fields  in  opposite  directions.  It  will  be  noticed 
that  while  the  patch  of  phosphorescence,  due  to  the  direct  rays, 


296]  CATHODE   RAYS.  509 

has  not  been  sensibly  broadened  by  the  magnetic  field,  the  narrow 
patch  due  to  the  'reflected'  rays  has  become  a  broad  band,  showing 
the  presence  of  some  rays  much  more  easily  deflected,  and  there- 
fore moving  more  slowly  than  the  incident  rays.  Since  one  of  the 
boundaries  of  the  reflected  patch  keeps  in  line  with  one  of  the 
direct  patch,  there  must  be  some  of  the  reflected  rays  which  move 
with  approximately  the  same  velocity  as  the  incident  rays. 

We  conclude  from  this  experiment  that  a  surface  struck  by 
cathode  rays  emits  secondary  rays  which  on  the  average  move 
more  slowly  than  the  primary  ones.  The  ratio  of  the  number 
of  secondary  to  the  number  of  primary  rays  is  greater  at  oblique 
than  at  normal  incidence.  The  'reflection'  of  cathode  rays  at 
the  surface  of  a  solid  seems  in  many  respects  analogous  to  the 
emission  of  corpuscles  from  a  body  illuminated  by  ultra-violet 
light.  The  corpuscles  in  the  primary  rays  penetrate  some  little 
distance  below  the  surface,  ionising  the  molecules  against  which 
they  strike ;  the  secondary  corpuscles  produced  in  this  way,  and 
perhaps  also  some  of  the  primary  ones  whose  motion  has  been 
reversed  by  the  collision  they  have  made  with  the  molecules 
of  the  reflector,  escape  from  the  reflector  and  form  the  reflected 
cathode  rays. 

The  path  of  a  corpuscle  which  strikes  the  reflector  obliquely 
will  be  nearer  the  surface  than  if  it  strikes  the  reflector  normally, 
arid  thus  the  corpuscles  liberated  by  it  will  have  a  shorter 
distance  to  travel  before  reaching  the  surface  of  the  reflector  and 
emerging  from  it,  we  should  therefore  expect  the  oblique  rays 
to  produce  more  reflected  rays. 

296.  Transmission  of  Cathode  Rays.  It  was  for  a  long  time 
believed  that  even  the  thinnest  slice  of  a  solid  was  impervious 
to  cathode  rays.  Thus  Goldstein  and  Crookes  had  shown  that 
bodies  as  thin  as  a  film  of  collodion  or  glass  blown  as  thin  as 
possible  cast  intensely  black  shadows  when  interposed  between 
the  cathode  and  the  walls  of  the  tube.  In  1892,  however,  Hertz* 
found  that  behind  a  piece  of  gold-leaf  or  thin  aluminium  foil 
there  was  appreciable  phosphorescence,  and  that  the  phosphor- 
escence was  deflected  by  a  magnet. 

*  Hertz,  Wied.  Ann.  xlv.  p.  28,  1892. 


510 


CATHODE   RAYS. 


[297 


297.  Lenard' s  Experiments.  Lenard*  made  a  series  of  most 
interesting  experiments  on  the  passage  of  cathode  rays  through 
very  thin  films.  The  rays  were  produced  in  a  tube  like  that 
represented  in  Fig.  170. 


Fig.  170. 

K,  the  cathode,  is  an  aluminium  disc  fastened  to  a  stiff  wire 
which  is  surrounded  by  a  glass  tube ;  the  anode  is  a  brass  tube 
surrounding  part  of  the  wire  carrying  the  cathode.  The  end  of 
the  tube  opposite  the  cathode  is  closed  by  a  metal  cap  fastened 
to  the  tube  by  marine-glue ;  a  hole  17  mm.  in  diameter  is  bored 
through  this  cap  and  covered  with  a  piece  of  thin  aluminium 
foil,  about  '00265  mm.  thick.  This  window  is  in  metallic  contact 
with  the  cap,  and  was  together  with  the  anode  connected  with 
earth.  The  tube  is  exhausted  until  the  difference  of  potential 
between  the  cathode  and  anode  is  very  great,  and  strong  cathode 
rays  reach  the  window.  In  a  dark  room  a  diffuse  light  spreads 
from  the  window  into  the  air  outside ;  this  light  is  brightest 
close  to  the  window,  its  outline  is  very  indefinite ;  with  a  strong 
discharge  in  the  tube  the  light  can  be  traced  to  some  centi- 
metres away  from  the  tube.  Phosphorescent  bodies  placed  in 
the  neighbourhood  of  the  window  phosphoresce.  In  air  at 
ordinary  pressures  the  rays  proceeding  from  the  window  diffuse 
*  Lenard,  Wied,  Ann.  li.  p.  225,  1894. 

\ 


298]  CATHODE   RAYS.  511 

out  very  rapidly,  and  shadows  cast  by  solid  bodies  placed  in  their 
path  are  ill  defined  and  many  times  larger  than  the  bodies  casting 
them.  These  rays  are  much  more  easily  studied  if  the  window, 
instead  of  opening  on  to  the  air,  opens  on  to  another  tube  from 
which  the  air  can  be  exhausted  :  when  the  air  in  this  tube  is 
at  a  low  pressure,  the  rays  travel  a  well-defined  path  and  can 
easily  be  studied.  The  rays  are  deflected  by  a  magnet,  by  an 
electric  field,  and  carry  a  negative  charge  of  electricity ;  the  ratio 
of  the  charge  to  the  mass  of  the  carrier  has  been  determined 
by  Lenard  (see  p.  95)  and  found  to  have  the  same  value  as  for 
cathode  rays.  These  facts  show  that  these  rays  are  cathode  rays ; 
it  is  often,  however,  convenient  to  distinguish  between  cathode 
rays  inside  and  outside  the  tube  producing  them ;  it  is  thus 
desirable  to  keep  the  term  Lenard  rays  for  the  latter  and  use 
cathode  rays  for  those  inside  the  tube. 

Lenard  measured  the  absorption  of  these  rays  by  various 
substances,  and  arrived  at  the  simple  law  connecting  absorption 
with  density,  already  discussed  on  p.  310.  Lenard  measured  the 
intensity  of  his  rays  by  the  phosphorescence  they  produced  in 
a  solution  of  pentadekylparatoleketone.  Seitz*,  who  has  made 
similar  measurements,  measured  the  total  charge  of  electricity 
carried  by  the  rays.  We  must  remember  that  unless  all  the  rays 
are  moving  with  the  same  velocity  the  two  methods  may  give 
different  results ;  in  the  electrical  method  all  the  corpuscles  count 
equally,  whatever  their  velocity  may  be;  in  the  optical  method, 
however,  this  is  no  longer  the  case,  the  more  rapidly  moving 
corpuscles  producing  much  more  phosphorescence  than  the  same 
number  of  corpuscles  with  smaller  velocity. 

298.  We  have,  when  considering  the  reflection  of  the  cathode 
rays,  supposed  that  the  incident  rays  gave  by  means  of  collisions 
sufficient  energy  to  some  of  the  corpuscles  in  the  metal  to  enaole 
them  to  escape  from  it.  In  the  case  of  reflection  we  have  to 
deal  with  the  corpuscles  which  emerge  from  the  face  of  the  metal 
first  struck  by  the  rays;  when,  however,  the  metal  is  very  thin, 
some  of  the  corpuscles  travelling  in  the  same  direction  as  the 
incident  rays  may  come  out  on  the  far  side  of  the  metal  and 
form  part  of  the  bundle  of  transmitted  rays;  many  of  these 
secondary  rays  will  be  moving  with  smaller  velocities  than  the 
*  Seitz,  Drude's  Ann.  iv.  p.  1,  1901. 


512  CATHODE   RAYS.  [299 

primary  rays,  and  thus  the  transmitted  rays  will  not  be  homo- 
geneous, and  the  electrical  and  optical  methods  of  estimating 
their  intensity  may,  as  explained  above,  give  different  results. 

299.  A  loss  of  velocity  in  the  rays  emerging  from  thin  plates 
of  metal  has  been  observed  by  Leithausers*  and  Des  Coudres  f%; 
the  latter  has  shown  also  that  the  patch  of  phosphorescence  due  to 
these  rays  is  under  the  action  of  a  magnetic  field  drawn  out  into 
a  broad  patch,  showing  that  the  transmitted  rays  are  not  homo- 
geneous (compare  the  corresponding  result  found  by  Gehrcke  for 
the  reflected  rays,  see  p.  508).     Des  Coudres  showed  also  that  the 
rays  which  emerge  obliquely  from  the  metal  have  smaller  velocities 
than  those  emerging  normally. 

300.  Scattering  of  Cathode  Rays  inside  the  tube.      Measure- 
ments of  the  scattering  of  cathode  rays  inside  the  discharge  tube 
have   been   made  by   Kaufmann  j,   who   employed   the   electrical 
method.     The  greatest  potential  differences  employed  was  only 
about  7500  volts,  so  that  the  velocity  of  the  rays  in  Kaufmann's 
experiments  was  very  much  less  than  in  those  of  Lenard.    The  prin- 
ciple of  the  method  used  by  Kaufmann  was  as  follows.     Consider 
a  bundle  of  rays  originally  horizontal  pfassing  through  the  gas,  then 
if  NQ  is  the  number  of  corpuscles  crossing  a  vertical  plane  AB  in 
unit  time,  the  number  crossing  a  parallel  plane  CD  at  a  distance  x 
from  AB  will  be  J\T0e~to,  where  b  is  by  definition  the  coefficient 
of  absorption ;    if   e   is    the  charge  carried  by  a  corpuscle    the 
quantity  of  negative  electricity  entering  the  space  between  AB 
and  CD  in  unit  time  is  NQe,  the  amount  leaving  it  is  N0ee~bx; 
hence   if   ABCD    is    surrounded    by    a    metallic    cylinder    the 
quantity   of    electricity   received   by   the  cylinder  in  unit   time 
is  N0e  (1  —  e~bx) ;   hence,  if  we  compare  the  charge  received  by 
the  cylinder  with  that  which  passes  through  the  end  CD,  we 
shall   find  (1  —  e"^)^"6*,  from  which  we  can  deduce  the  value 
of  b.     Kaufmann  in  this   way  determined   6   for  nitrogen,  car- 
bonic oxide,  carbonic  acid  and   hydrogen,  at  pressures  ranging 
from   about    1/50    to    1/28    of    a    millimetre   of    mercury   and 
with  potential  differences  from  about   2500  to  7500  volts ;   he 

*  Leithausers,  Site.  Berlin.  Akad.  d.  Wissensch.  Mar.  13,  1902. 
t  Des  Coudres,  Phys.  Zeits.  iv.  p.  140,  1902. 
£  Kaufmann,  Wied.  Ann.  Ixix.  p.  95,  1899. 


301]  CATHODE  RAYS.  513 

found  that  if  V  is  the  potential  difference  in  the  discharge  tube 
in  volts,  p  the  pressure  in  millimetres  of  mercury,  then  for  the 
same  gas,  within  the  limits  of  pressure  and  potential  difference 
indicated,  bV/p  was  constant;  i.e.  the  absorption  coefficient  is 
proportional  to  the  pressure  and  inversely  proportional  to  the 
kinetic  energy  of  the  corpuscle.  The  values  for  the  different 
gases  are  indicated  in  the  following  table  : 

Gas  bV/p  Molecular  weight 

H2  730  2 

N2  5650  28 

CO  6380  28 

C02  6830  44 

The  values  of  b  do  not  follow  those  of  the  molecular  weight 
as  closely  as  the  values  determined  by  Lenard ;  one  reason  for  this 
may  be  the  greater  velocities  of  the  rays  investigated  by  Lenard ; 
we  have  seen  (p.  315)  that  it  is  only  for  very  rapidly  moving 
cathode  rays  that  we  could  expect  Lenard's  law  to  be  strictly  true  ; 
another  reason  may  be  that  in  the  method  used  by  Kaufmann 
the  positive  and  negative  ions  produced  by  the  primary  rays 
by  collision  with  the  molecules  of  the  gas  might  diffuse  with 
different  velocities  to  the  conductors  in  the  tube,  so  that  part 
of  the  current  measured  in  these  experiments  may  be  due  to 
secondary  ionisation. 

301.  Magnetic  Spectrum  of  Cathode  Eays.  Birkeland  *  found 
that  when  the  cathode  rays  are  produced  by  means  of  an  in- 
duction coil,  a  patch  of  cathodic  phosphorescence  is  not  merely 
displaced  by  a  magnetic  field,  but  is  broken  up  into  several 
distinct  patches;  thus,  for  example,  if  there  is  originally  a 
narrow  straight  band  of  phosphorescence,  then  under  the  magnetic 
field  several  parallel  bright  bands  of  phosphorescence  separat  -d 
by  comparatively  dark  spaces  are  observed.  This  is  called  the 
magnetic  spectrum.  I  have  obtained  similar  effects  by  deflecting 
the  rays  by  electric  instead  of  magnetic  forces.  This  splitting 
up  of  the  rays  shows  that  the  original  bundle  of  cathode  rays 
is  not  homogeneous,  but  is  made  up  of  groups  moving  with 
different,  and  finitely  different,  velocities;  each  group  being 
differently  deflected,  the  slower  ones  more  than  the  faster. 

*  Birkeland,  Comptes  Rendus,  cxxiii.  p.  92,  1897. 
T.  G.  33 


514  CATHODE  RAYS.  [302 

Strutt*  has  shown  that  the  magnetic  spectrum  is  due  to  the 
want  of  uniformity  necessarily  associated  with  the  use  of  an 
induction  coil,  which  produces  a  discontinuous  discharge,  and  that 
if  the  cathode  rays  are  produced  by  a  large  electrostatic  machine, 
or  a  large  number  of  storage  cells,  either  of  which  gives  a  con- 
tinuous discharge,  the  phosphorescence  is  not  broken  up  into 
separate  patches  by  a  magnetic  or  an  electric  field. 

302.  Path  of  the  Cathode  Rays  in  the  Discharge  Tube.  The 
cathode  rays  are  deflected  by  an  electric  force;  thus,  as  the 
electric  field  is  very  intense  in  the  Crookes  dark  space,  the  rays 
as  they  pass  through  this  space  will,  unless  the  lines  of  force  in 
it  are  straight  (this  is  approximately  the  case  when  the  cathode 
is  a  large  plane  disc),  be  deflected  and  their  paths  will  not 
coincide  with  the  normals  to  the  cathode  at  their  point  of 
projection.  The  amount  of  deflection  of  the  path  from  this 
normal  will  depend  mainly  upon  the  rate  at  which  the  intensity 
of  the  electric  field  diminishes  as  we  recede  from  the  cathode : 
if,  as  in  the  case  when  the  pressure  is  not  very  low,  the  field 
close  to  the  cathode  is  very  much  more  intense  than  that  at 
some  distance  away  from  it,  the  corpuscles  will  acquire  so  much 
energy  while  still  close  to  the  cathode  that  they  will  not  be 
much  deflected  by  the  comparatively  feeble  fields  traversed  by 
J-hein  during  the  rest  of  the  journey;  in  this  case  the  paths  of 
the  rays  will  be  approximately  the  normals  to  the  cathode,  so 
that  if  the  cathode  is  a  hollow  spherical  bowl  the  rays  will  travel 
along  the  radii  of  the  sphere  and  will  be  brought  to  a  focus  at 
its  centre.  If  however  the  strength  of  the  field  only  changes 
slowly  as  we  recede  from  the  cathode,  we  shall  get  much 
greater  deviation  than  in  the  last  case,  for  not  only  will  the 
velocity  they  acquire  while  still  close  to  the  cathode  be  smaller, 
but  also  the  deflecting  force  when  they  get  away  from  the 
cathode  will  be  greater.  The  paths  of  the  rays  will  now  be  no 
longer  along  the  normals  because  of  the  deflecting  force,  nor  will 
they,  owing  to  the  inertia  of  the  corpuscles,  be  along  the  lines 
of  force  unless  these  are  straight.  The  paths  of  the  corpuscles 
will  be  between  the  normal  and  the  lines  of  force  ;  thus,  for 
example,  in  the  case  of  the  hollow  bowl,  the  path  will  be  between 
the  normal  CP  and  the  line  of  force  PQ  (Fig.  171);  thus,  if  the 

*  Strutt,  Phil.  Mag.  v.  48,  p.  478,  1899. 


304]  CATHODE  RAYS.  515 

paths  cross  the  axis  of  the  bowl  at  all,  they  will  do  so  at  points 
on  the  far  side  of  the  centre.     It  is  well  known  that  when,  as  in 


Fig.  171. 

the  bulbs  used  for  producing  Rontgen  rays,  a  cathode  of  this  kind 
is  used,  the  '  focus'  gets  further  from  the  cathode  as  the  ex- 
haustion is  increased.  Goldstein*,  who  made  a  series  of  beautiful 
experiments  on  the  phosphorescent  patterns  produced  by  curved 
cathodes  of  different  shapes,  showed,  by  using  an  unsymmetrical 
cathode,  that  the  rays  crossed  when  the  pressure  was  com- 
paratively high,  but  did  not  do  so  at  very  high  exhaustions. 
The  appearance  of  the  cathode  rays  from  a  curved  cathode  is 
shown  by  the  diagrams  in  Fig.  173  taken  from  a  paper  by 
Campbell  Swintonf;  it  will  be  seen  that  this  is  very  different 
from  that  which  would  result  if  the  rays  travelled  along  the 
normals  to  the  cathode. 

303.  The  motion  of  the  corpuscles  in  a  vacuum  tube  offers  a 
fine  field  for  the  application  of  Hamilton's  Principle  of  Varying; 
Action :  for  since  the  cathode  is  an  equipotential  surface,  and  the 
corpuscles  leave  that  surface  normally  and  with  equal  amounts  of 
energy,  their  paths  will,  by  the  Principle  of  Varying  Action,  be 
the  orthogonal  trajectories  of  a  system  of  surfaces. 

304.  We  have  regarded  the  cathocle  rays^  as  originating  from 
positive  ions  which  were  formed  by  the  cathode  rays  themselves 

*  Goldstein,  Wied.  Ann.  xv.  p.  254,  1882. 

t  Campbell  Swinton,  Proc.  Roy.  Soc.  Ixi.  p.  79,  1897. 

33—2 


516  CATHODE   RAYS.  [304 

at  a  distance  from  the  cathode.  If  however  the  path  PQ  of  the 
cathode  ray  is  curved  (Fig.  172),  and  if  the  positive  ion  is  pro- 
duced at  Q,  then,  in  consequence  of  the  difference  in  mass  between 


Fig.  172. 

the  positive  and  negative  ions,  the  path  of  the  positive  ion  up 
to  the  cathode  will  not  be  QP,  but  some  other  path  such  as  QP' ; 
thus  the  cathode  rays  produced  at  P  will,  when  the  paths  are 
not  straight  lines,  give  rise  to  positive  ions  which  will  help  to 
make  cathode  rays  which  start  not  from  P  but  from  some  other 
point  P'. 

The  distance  between  the  places  where  the  positive  ions 
strike  the  cathode  and  the  origin  of  the  cathode  ray  producing 
these  ions  will  be  greatest  for  the  rays  which  start  from  near 
the  boundary  of  the  cathode,  as  these  travel  through  the  part 
of  the  electric  field  where  the  lines  of  force  are  most  curved; 
there  will  thus  not  be  many  positive  ions  striking  against  the 
outer  parts  of  the  cathode,  on  this  account  the  rate  of  emission 
of  the  cathode  rays  increases  as  we  approach  the  centre  of  the 
cathode ;  on  the  other  hand,  if  the  cathode  is  curved  the  electric 
force  close  to  the  cathode  will  be  a  minimum  at  the  centre,  so 
that  on  this  account  the  rays  would  be  fewer  along  the  axis; 
taking  both  these  effects  into  consideration  we  should  expect 
there  would  be  a  tendency  for  the  rays  to  attain  a  maximum 
at  some  place  intermediate  between  the  centre  and  edge  of  the 
cathode. 


305]  CATHODE  RAYS.  517 

The  observations  of  Campbell  Swinton*  establish  the  existence 
of  such  an  effect;  he  found  that  with  concave  cathodes,  when 
the  pressure  of  the  gas  is  within  certain  limits,  the  cathode  rays 
do  not  form  a  solid  pencil  but  are  condensed  into  a  hollow  conical 
shell.  He  proved  this  by  means  of  the  phosphorescence  produced 
by  these  rays  on  a  carbon  plate  whose  plane  was  at  right  angles 
to  the  cathode  :  the  phosphorescent  patch  was  a  circular  ring 
with  in  some  cases  a  bright  spot  at  the  centre.  The  appearance 
of  the  phosphorescence  is  represented  in  Fig.  173. 


T   T   T 


Fig.  173. 

This  hollowness  of  the  bundle  of  cathode  rays  was  found  by 
Campbell  Swinton  to  depend  on  the  curvature  of  the  cathode,  it 
did  not  occur  when  this  was  plane. 

305.  Repulsion  of  Cathodic  Streams.  Goldstein  f  found  that 
when  in  a  discharge  tube  there  are  two  cathodes  connected 
together,  the  cathodic  rays  from  one  cathode  are  deflected  when 
they  pass  through  the  dark  space  surrounding  the  other  cathode. 

One  of  Goldstein's  experiments  was  as  follows:  one  of  the 
cathodes  was  a  hollow  metal  cylinder  a,  from  which  a  pencil  of 
cathode  rays  issued,  producing  luminosity  in  the  gas  through 

*  Campbell  Swinton,  Proc.  Roy.  Soc.  Ixi.  p.  79,  1897. 
t  Goldstein,  Eine  neue  Form  der  elektrischen  Abstossung. 


518  CATHODE   RAYS.  [305 

which  they  travelled ;  the  other  cathode  (b)  was  a  wire  at  right 
angles  to  the  axis  of  the  bundle  of  rays  proceeding  from  a ;  when 


Fig.  174. 

6  was  disconnected  from  a  the  path  of  the  rays  from  a  was 
straight,  but  when  a  and  b  were  connected  the  cathode  rays 
from  a  were  bent  sharply  away  when  they  approached  b.  Gold- 
stein found  that  the  amount  of  deflection  did  not  depend  on 
the  material  of  which  the  cathodes  were  made,  nor  on  the  nature 
of  the  gas  through  which  the  rays  passed.  The  deflection  ceased 
if  the  deflecting  cathode  was  surrounded  by  a  screen  of  some 
solid  substance. 

Another  example  of  the  deflection  of  two  cathode  streams  is 
afforded  by  an  experiment  made  by  Crookes*;  a  and  b  (Fig.  175) 
are  two  metal  discs,  either  or  both  of  which  can  be  made  into 


Fig.  175. 

cathodes,  a  diaphragm  with  two  holes  cut  in  it  is  placed  in  front  « 
of  these  discs,  and  the  path  of  the  rays  through  the  tube  is 
marked  out  by  the  phosphorescence  they  excite  in  a  chalked 
plate  inclined  at  a  small  angle  to  their  path.  When  a  is  the 
cathode  and  6  is  idle  the  rays  travel  along  the  path  df,  while  when 
a  is  idle  and  b  the  cathode  they  travel  along  ef.  When,  however, 
*  Sir  W.  Crookes,  Phil.  Trans.  1879,  part  ii.  p.  652. 


306]  CATHODE   RAYS.  519 

a  and  b  are  cathodes  simultaneously  the  paths  of  the  rays  are 
dg  and  eh  respectively,  the  two  streams  having  apparently  re- 
pelled each  other.  Crookes  attributed  the  divergence  of  the  rays 
to  the  repulsion  between  the  negative  charges  of  electricity 
travelling  along  with  them.  E.  Wiedemann  and  Ebert*,  however, 
by  a  modification  of  this  experiment,  have  shown  that  this  is 
not  the  cause  of  the  repulsion ;  they  provided  the  holes  d  and  e 
with  shutters,  and  found  that  when  a  and  b  were  simultaneously 
cathodes  eh  was  the  path  of  the  rays  through  e,  whether  the 
window  at  d  was  open  or  shut,  although  when  it  was  shut  there 
were  of  course  no  cathode  rays  travelling  along  dg  to  deflect  those 
passing  through  d,  showing  that  the  deflection  of  the  rays  has 
its  origin  in  the  space  between  a  and  d. 

The  effects  we  have  been  describing  can  all  be  explained  by 
the  electrostatic  repulsion  of  the  negative  electricity  travelling 
along  the  cathode  rays,  by  the  strong  electric  field  which  sur- 
rounds a  cathode;  this  repulsion  is  appreciable  only  when  the 
rays  from  one  cathode  pass  through  the  dark  space  of  the  de- 
flecting cathode,  because,  as  we  have  seen,  the  intensity  of  the 
electric  field  is  very  much  greater  in  the  dark  space  than  it  is 
at  any  other  part  of  the  discharge ;  we  have,  on  page  435, 
discussed  a  method  of  using  this  deflection  of  the  cathode  rays 
for  measuring  the  strength  of  the  electric  field  in  the  tube. 

306.  Canalstrahlen  or  Positive  Rays.  When  a  perforated 
cathode  is  used,  there  may,  if  the  pressure  is  between  certain 
limits,  be  observed  luminous  streams  passing  through  the  holes  in 


the  cathode,  emerging  on  the  side  of  the  cathode  remote  from  the 

anode,  and  travelling  in  straight  lines,  as  in  Fig.  176;  these  were 

*  Wiedemann  and  Ebert,  Wied.  Ann.  xlvi.  p.  158,  1891. 


520  CATHODE  RAYS.  [306 

first  observed  by  Goldstein*,  and  called  by  him  Canal strahlen. 
They  excite  phosphorescence  on  the  part  of  the  glass  against  which 
they  strike,  and  if  this  glass  is  soda  glass  the  places  struck  by  these 
rays  show,  when  observed  through  the  spectroscope,  the  sodium 
lines.  Wehnelt-f-  has  shown  that  when  these  rays  strike  against 
a  copper  plate  they  oxidise  it ;  the  cathode  rays,  as  we  have  seen 
(p.  496),  reduce  an  oxidised  plate.  Schmidt J  has  shown  that  the 
oxidation  of  metals  by  the  Canalstrahlen  is  not  due  to  the  impact 
of  the  rays  but  is  an  indirect  effect  due  to  the  rays  producing 
active  oxygen  when  they  pass  through  the  gas ;  he  showed  this  by 
casting  a  shadow  on  the  copper  plate  by  interposing  between  it 
and  the  rays  a  solid  obstacle,  the  part  of  the  plate  in  shadow  was 
as  much  oxidised  as  that  exposed  to  the  direct  impact  of  the  rays. 
In  hydrogen  Schmidt  observed  that  the  Canalstrahlen  exert  a 
reducing  effect. 

Though  these  rays  are  much  less  deflected  than  the  cathode 
rays  by  electric  and  magnetic  fields,  they  do  suffer  appreciable 
deflection,  and  W.  Wien  has  shown  (see  p.  117)  that  the  direction 
of  these  deflections  indicates  that  the  Canalstrahlen  consist  of  posi- 
tively charged  particles ;  he  has  measured,  by  the  method  indicated 
in  Chap.  V.,  the  ratio  of  the  charge  to  the  mass,  and  finds  for  the 
maximum  value  of  this  quantity  104,  which  is  the  ratio  of  the 
charge  to  the  mass  for  the  hydrogen  ion  in  the  electrolysis  of 
solutions.  Wien  found  that,  in  addition  to  the  rays  which  give 
this  limiting  value  to  e/m,  there  were  always  other  rays  present 
which  gave  smaller  values  for  e/m,  and  that  there  was  no  evidence 
that  the  change  in  this  quantity  was  discontinuous,  which  it 
would  be  if  the  charge  could  only  change  by  multiples  of  e 
and  the  mass  by  multiples  of  ra.  I  have  observed  similar 
variations  in  the  value  of  e/m  for  the  positive  ions  given  off 
from  incandescent  wires ;  I  think  this  variation  is  probably  due 
to  the  positive  ions  losing  their  charges  before  they  reach  the 
glass  where  they  produce  phosphorescence ;  what  is  measured  in 
these  determinations  is  ratio  of  the  mean  value  of  e^to  m ;  if 
now  the  positive  ion  gets  neutralised  by  a  negative  charge  before 
it  reaches  the  glass,  then  the  mean  value  of  e  would  be  smalleK 

*  Goldstein,  Berlin  Sitz.  xxxix.  p.  691,  1886 ;  Wied.  Arm.  Ixiv.  p.  45,  1898. 
t  Wehnelt,  Wied.  Ann.  Ixvii.  p.  421,  1899. 
t  Schmidt,  Drude's  Ann.  ix.  p.  703,  1902. 


307]  CATHODE   RAYS.  521 

than  if  it  retained  its  charge  up  to  the  moment  of  impact.  We 
must  remember  that  the  gas  through  which  the  Canalstrahlen 
move  is  ionised,  and  that  there  are  plenty  of  corpuscles  about 
to  neutralise  the  positive  charge.  It  may  be  urged  that  if  the 
ions  had  lost  their  charge  before  striking  the  glass,  they  would 
not  be  able  to  produce  phosphorescence,  since,  as  far  as  our 
knowledge  extends,  phosphorescence  is  not  produced  by  the  im- 
pact of  uncharged  molecules;  but,  according  to  Wien's  deter- 
mination, the  positive  ions  in  the  Canalstrahlen  are  moving  with 
a  velocity  of  more  than  108cm./sec.:  we  have  no  experience  of 
molecules  moving  with  anything  like  this  velocity;  the  shock  of 
the  collision  might  be  sufficient  to  ionise  the  molecule  afresh, 
and  thus  produce  in  the  neighbourhood  of  the  place  of  impact 
effects  analogous  to  those  produced  by  the  collision  of  charged  ions. 

307.  Several  experiments  have  been  made  by  W.  Wien*, 
Ewers "f  and  Villardj;  to  detect  the  positive  charge  carried  by  the 
Canalstrahlen  by  catching,  as  in  Perrin's  experiment  on  the 
negative  charge  carried  by  the  cathode  rays  (see  p.  502),  the 
Canalstrahlen  in  a  Faraday  cylinder,  and  observing  the  charge 
acquired  by  that  cylinder.  The  aforesaid  physicists  differ  in  their 
interpretation  of  the  results  they  obtain;  all  agree  that  under 
certain  circumstances  the  Faraday  cylinder,  placed  behind  a  per- 
forated cathode,  receives  a  positive  charge  of  electricity,  but 
while  Wien  and  Ewers  think  that  this  charge  is  carried  by  the 
Canalstrahlen,  Villard  is  of  opinion  that  it  is  a  secondary  effect 
due  to  the  slow  diffusion  into  the  cylinder  of  ions  from  other 
parts  of  the  tube.  In  his  experiments  he  found  that  the 
Canalstrahlen  were  able  to  penetrate  into  the  cylinder  for  some 
time  before  it  gave  any  indication  of  a  positive  charge,  indeed 
if  the  charge  only  lasted  a  short  time,  the  positive  charge  in 
the  cylinder  first  appeared  some  little  time  after  the  discharge 
had  stopped.  It  seems  possible  that  while  the  discharge  is 
passing  the  gas  in  the  tube  is  too  good  a  conductor  to  allow 
the  charge  on  the  cylinder  to  accumulate;  just  as  in  Perrin's 
experiment  the  conductivity  of  the  gas  prevents  the  negative 
charge  on  the  cylinder  rising  above  a  certain  value,  however 

*  W.  Wien,  Wied.  Ann.  Ixv.  p.  445,  1898. 

t  Ewers,  Wied.  Ann.  Ixix.  p.  167,  1899. 

J  Villard,  Journal  de  Physique,  [3],  t.  viii.  pp.  5  and  140,  1899. 


522  CATHODE  RAYS.  [307 

long  the  cathode  rays  are  kept  playing  on  the  cylinder;  when 
the  discharge  stops,  the  gas  recovers  its  insulating  power,  and 
the  cylinder  can  retain  any  charge  that  diffuses  into  it ;  if  this 
view  is  correct,  the  positive  charge  observed  in  the  cylinder  is 
due  mainly,  at  any  rate,  to  diffusion  and  not  to  convection  by  the 
Canalstrahleri. 

In  spite  of  the  indecisive  results  obtained  by  this  experi- 
ment, the  magnetic  and  electric  deflections  obtained  by  W.  Wien 
seem  conclusive  evidence  that  the  Canalstrahlen  carry  a  positive 
charge. 

On  the  view  of  the  discharge  given  in  Chap.  XVI.  there  is 
a  stream  of  positively  charged  molecules  moving  towards  the 
cathode,  causing  this  to  emit  cathode  rays ;  if  the  cathode  is 
perforated,  part  of  this  stream  may  pass  through  the  holes, 
producing  in  the  gas  behind  the  cathode  luminosity,  forming 
in  fact  the  Canalstrahlen,  or  positive  rays  as  we  may  call  them, 
if  we  think  this  view  of  their  constitution  sufficiently  established. 


CHAPTER  XVIII. 

EONTGEN  RAYS. 

308.  RONTGEN  found  in  1895  that  when  the  pressure  in  a 
discharge  tube  is  so  low  that  the  walls  of  the  tube  are  vividly  phos- 
phorescent, rays  which  are  propagated  in  straight  lines  come  from 
the  tube ;  these  rays  illuminate  a  screen  made  of  phosphorescent 
substance,  and  affect  a  photographic  plate  placed  in  their  path. 
Rontgen  showed  too  that  these  rays  were  not  entirely  stopped 
even  by  substances  opaque  to  ordinary  light,  such  as  the  flesh 
of  the  hand,  and  that  if  the  hand  is  placed  between  the  bulb 
and  a  phosphorescent  screen,  the  shadow  cast  by  the  flesh  is  not 
so  dark  as  that  cast  by  the  bones,  and  thus  the  shape  of  the 
latter  can  be  distinguished.  The  rays  which  produce  these  effects 
are  now  called  Rontgen  rays.  The  character  of  the  rays  de- 
pends greatly  upon  the  state  of  the  tube  in  which  they  are 
produced  ;  if  the  pressure  in  the  tube  is  very  low,  so  that  the 
potential  difference  between  its  terminals  is  very  large,  the  rays 
are  much  more  penetrating  than  when  the  pressure  of  the  gas 
is  higher,  and  the  potential  difference  between  its  electrodes 
smaller;  very  penetrating  rays  are  sometimes  called  hard  rays, 
the  more  easily  absorbable  rays,  soft  ones.  We  have  already  seen 
that  even  the  rays  emitted  at  any  one  time  by  the  same  \,abe 
are  not  all  of  one  type  (see  p.  246). 

We  have  already  discussed  a  good  many  of  the  properties 
of  the  Rontgen  rays  in  connection  with  the  power  they  possess 
of  ionising  a  gas  through  which  they  pass ;  we  shall  now  consider 
the  other  properties  of  these  rays. 

Rontgen  showed,  and  the  observation  has  been  confirmed  by 
very  many  subsequent  experimenters,  that  the  rays  are  not  bent 


524  RONTGEN   RAYS.  [309 

when  going  from  one  medium  to  another,  and  therefore  that  they 
suffer  no  deviation  after  passing  through  a  solid  prism. 

We  have  seen  (p.  258)  that  Rontgen  rays  when  they  strike 
against  a  solid,  a  liquid,  or  even  a  gas,  generate  secondary  rays 
which  in  the  case  of  impact  against  a  solid  or  a  liquid  are 
of  a  much  less  penetrating  character  than  the  incident  ones ; 
the  incidence  of  Rontgen  rays  on  the  surface  of  a  solid  will 
therefore  give  rise  to  radiation  proceeding  from  the  surface ;  by 
far  the  greater  part  of  this  'reflected'  radiation  is  diffuse,  i.e. 
though  the  incident  rays  are  all  travelling  in  one  direction,  the 
' reflected'  rays  will  spread  out  in  all  directions.  The  question 
as  to  whether  this  'diffuse  return'  of  the  rays, -as  Sir  George 
Stokes  called  it,  is  accompanied  by  specular  reflection,  in 
other  words,  whether  there  is  an  excess  of  the  reflected  rays 
in  the  direction  in  which  the  angle  of  reflection  is  equal  to  the 
angle  of  incidence,  is  one  on  which  observers  disagree.  Lord 
Blythswood*  and  Rood'f  have  obtained  photographs  in  which 
there  is  evidence  of  this  effect ;  other  observers  have,  however, 
been  unable  to  detect  it.  The  specular  reflection  must  in  any 
case  be  small,  since  the  transparency  of  a  powder  is  the  same 
as  that  of  the  same  bulk  of  material  when  solid,  and  the  defini- 
tion through  it  as  good. 

No  evidence  of  any  polarisation  of  the  rays  has  been  obtained ; 
the  opacity  of  two  crystals  of  tourmaline  or  of  herapathite,  placed 
one  on  the  top  of  the  other,  is  the  same  when  the  axes  of  the 
crystals  are  crossed  as  when  they  are  parallel. 

The  Rontgen  rays  increase  the  electrical  conductivity  of  badly 
conducting  liquids  as  well  as  of  gases J,  they  increase  also  the 
electric  absorption  of  solids.  Curie  §  has  lately  shown  that  the 
rays  from  radium  also  produce  the  same  effect  on  liquids. 

309.  Source  of  the  Rays.  By  taking  photographs  of  a  card 
pierced  with  pinholes,  and  drawing  the  lines  joining  the  photo- 
graph of  a  hole  with  the  hole  itself,  and  finding  their  points  of 
intersection,  it  has  been  shown  that  the  spot  struck  by  the 
cathode  rays  is  the  place  from  which  the 'Rontgen  rays  originate. 

*  Lord  Blythswood,  Proc.  Roy.  Soc.  lix.  p.  330,  1896. 
t  Eood,  Silliman's  Journal,  [4],  ii.  p.  173,  1896. 
J  J.  J.  Thomson,  Nature,  Iv.  p.  606,  1897. 
§  Curie,  Comptes  Rendus,  cxxxiv.  p.  420,  1902. 


310]  RONTGEN   RAYS.  525 

Thus  when  the  rays  strike  the  walls  of  the  tube,  the  phosphor- 
escent part  of  the  glass  is  the  origin  of  the  rays ;  when  a  '  focus 
tube,'  i.e.  one  with  a  hollow  cathode,  and  a  plate  of  some  infusible 
substance  placed  where  the  cathode  rays  converge,  the  part  of  the 
plate  struck  by  the  cathode  rays  is  the  source  of  the  Rontgen  rays. 
Campbell  Swinton*  has  shown  that  cathode  rays  impinging 
normally  on  the  plate  are  more  effective  in  producing  Rontgen  , 
rays  than  those  which  strike  obliquely  against  the  plate.  The  ' 
Rontgen  rays  produced  when  the  cathode  rays  strike  against 
a  plane  area  come  off  approximately  uniformly  in  all  directions. 
This  is  shown  by  the  folio  wing  experiment:  a  hemispherical  photo- 
graphic film  is  placed  so  that  its  centre  is  at  G,  a  point  on  a  metal 
plate  struck  by  cathode  rays  travelling  in  any  direction ;  the 
Rontgen  rays  starting  from  the  f)late  affect  the  film,  and  when 
the  photograph  is  developed  its  intensity  is  found  to  be  approxi- 
mately uniform  until  we  approach  quite  close  to  the  line  where 
the  plane  of  the  plate  intersects  the  film.  When  the  rays  are 
produced  by  the  impact  of  the  cathode  rays  against  the  glass 
walls  of  the  tube  more  rays  appear  to  come  out  from  any  place 
normally  than  obliquely ;  this  is,  however,  a  secondary  effect  due 
to  the  absorption  of  the  rays  by  the  glass  through  which  they 
have  to  pass ;  as  the  rays  which  come  out  obliquely  have  to  pass 
through  a  greater  thickness  of  glass  than  those  which  emerge 
normally  they  are  more  enfeebled  by  the  absorption  due  to  the 
glass. 

310.  Velocity  of  Propagation  of  Rontgen  Rays.  Experiments 
to  determine  the  velocity  of  the  Rontgen  rays  have  been  made 
by  Brunhesf  and  Blondlotj.  The  property  used  in  each  distance 
to  detect  the  rays  was  the  effect  these  rays  have  in  facilitating 
the  passage  of  a  spark.  This  property,  it  must  be  confessed, 
does  not  seem  well  fitted  for  the  purpose;  for  since  the  effect 
of  the  rays  on  the  spark  is  due  to  the  ionisation  of  the  gas 
close  to  the  spark  gap,  and  as  the  gas  when  once  ionised  would 
remain  so  for  an  appreciable  time,  the  effect  of  the  rays  on  the 
spark  might  persist  for  some  time  after  the  rays  had  stopped, 
and  thus  the  brightening  of  the  spark  by  the  rays  is  not 

*  Campbell  Swinton,  Proc.  Roy.  Soc.  Ixiii.  p.  432,  1898. 
f  Brunhes,  Comptes  Eendus,  cxxx.  p.  169,  1900. 
J  Blondlot,  Comptes  Rendus,  cxxxv.  p.  666,  1902. 


.526  RONTGEN   RAYS.  [310 

conclusive  evidence  that  the  rays  fall  on  the  spark  gap 
simultaneously  with  the  passage  of  the  spark.  The  method 
adopted  by  Blondlot,  in  his  experiments  which  have  just 

H' 


A' 

B' 

7 
c 

D\ 

I 

A    "" 
Fig.  177. 

B 

been  published,  is  indicated  by  the  diagram  in  Fig.  177.  B,  B' 
are  the  terminals  of  the  secondary  of  an  induction  coil,  these 
are  connected  with  the  plates  A  and  A'  of  a  Hertz  radiator,  and 
to  the  terminals  H  and  Hf  of  a  tube  exhausted  sufficiently  to 
emit  Rontgen  rays.  A  resonator  made  of  copper  wire  folded  into 
a  triangle  ODD'  is  placed  beneath  the  radiator.  The  spark  gap 
C  of  the  resonator  is  placed  so  that  it  receives  Rontgen  rays  from 
the  tube  HH',  but  is  protected  from  all  other  radiation  by 
screens  of  black  paper  and  an  aluminium  plate.  The  radiator 
AA'  consists  of  two  horizontal  brass  cylinders  immersed  in  vase- 
line oil.  The  view  taken  by  Blondlot  of  the  action  of  this 
apparatus  is  as  follows :  when  the  current  in  the  primary  of  the 
induction  coil  is  broken  the  difference  of  potential  between  H 
and  H'  increases  until  it  is  sufficient  to  send  a  discharge  through 
the  tube  and  cause  it  to  emit  Rontgen  rays ;  when  the  potential 
difference  increases  a  little  further  a  spark  passes  between  A  and 
A,  short  circuiting,  as  it  were,  this  circuit  and  extinguishing  the 
discharge  through  the  tube  HH'.  The  length  of  the  gap  between 
A  and  A  was  adjusted  so  that  the  potential  required  to  produce 
the  spark  was  only  slightly  greater  than  that  required  to  send 
a  discharge  through  the  tube,  so  that  the  tube  was  extinguished 
very  soon  after  the  spark  commenced  and  the  radiator  commenced 
to  vibrate.  The '  electromotive  force  round  the  resonator  will  be 
still  longer  in  rising  to  a  value  great  enough  to  spark  across  (7, 
so  that,  if  the  tube  is  close  to  C,  the  Rontgen  rays  will  have 
left  C  long  before  the  spark  passes,  and  thus  if  the  effect  of  the 
rays  on  the  spark  is  confined  to  the  time  when  the  rays  are 
actually  falling  on  the  spark  gap  the  rays  will  have  no  influence 
upon  the  spark.  Blondlot  found  that  in  this  case  the  sparks  are 


310]  RONTGEN    RAYS.  527 

not  affected  by  placing  a  lead  plate  between  the  tube  HH'  and 
the  spark  gap  G.  If  now  long  wires  are  inserted  between  A  and  H 
and  A1  and  H',  the  extinction  of  the  rays  in  the  tube  HH'  will 
take  place  at  a  longer  interval  after  the  commencement  of  the 
spark  between  A  and  A',  and  if  the  wires  are  sufficiently  long 
the  delay  may  be  so  great  that  the  spark  may  have  commenced  at 
C  before  the  rays  have  ceased  to  fall  upon  the  spark  gap,  so  that 
the  rays  may  increase  the  brilliancy  of  the  spark;  in  this  case 
Blondlot  found  that  the  interposition  of  a  lead  plate  diminished 
the  brightness  of  the  spark.  The  arrival  of  the  rays  at  the  spark 
gap  can  also  be  delayed  by  moving  the  tube  HH'  away,  keeping 
the  lengths  of  wire  between  A  and  H  and  A'  and  H'  constant, 
but  uncoiling  the  wire  so  as  to  allow  of  the  motion  of  HH'. 
Blondlot  found  that  moving  the  tube  away  increases  the  bright- 
ness of  the  sparks  when  the  Rontgen  rays  fall  on  the  spark  gap, 
but  when  the  rays  are  stopped  by  a  lead  plate  the  motion  of 
the  tube  has  no  effect  upon  the  sparks.  When  the  tube  is  just 
so  far  away  from  the  gap  that  the  rays  pass  through  the  gap 
during  the  whole  of  the  time  the  sparks  are  passing  across  (7, 
the  effect  of  the  rays  will  be  a  maximum,  for  increasing  the 
distance  of  the  tube  from  the  gap  will  dimmish  the  intensity 
of  the  rays  at  the  spark  gap  without  increasing  the  time  during 
which  they  and  the  electric  field  act  together  at  the  gap  :  pushing 
the  tube  nearer  the  gap  diminishes  the  time  of  conjoint  action 
of  the  rays  and  field  at  the  spark  gap.  Let  us  suppose  that  the 
tube  is  in  such  a  position  that  the  sparks  are  at  their  brightest, 
and  suppose  now  that  the  length  of  the  wires  between  A  and  H 
and  also  between  A'  and  H'  is  shortened  by  a  length  I ;  let  V 
be  the  velocity  of  propagation  of  an  electrical  disturbance  along 
a  wire,  then  if  we  suppose  that  the  extinction  of  the  bulb  HH' 
is  due  to  the  propagation  of  the  drop  of  potential  at  A  A'  pro- 
duced by  the  short  circuiting  of  this  circuit  by  the  spark,  ;he 
rays  will  terminate  at  the  time  l/V  earlier  than  they  did  before ; 
if  they  were  just  contemporaneous  with  the  force  at  the  gap 
before,  they  can  be  made  so  again  by  moving  the  tube  a  distance 
I'  further  from  the  gap  without  altering  the  length  of  the  wires, 
provided  I'/V'—l/V,  where  V  is  the  velocity  of  Rontgen  rays 
through  air;  provided  also  that  the  lengthening  of  the  wires 
and  the  displacement  of  the  tube  does  not  affect  the  magnitude 
and  duration  of  the  forces  acting  on  the  spark  gap.  Blondlot's 


528    .  BONTGEN  KAYS.  [311 

method  is  then  to  start  with  the  bulb  in  the  position  in  which 
the  sparks  are  brightest,  shorten  or  lengthen  the  wires  AH  and 
A'H'  by  I,  and  then  measure  the  distance  I'  through  which  he 
has  to  displace  the  tube  until  the  brightness  of  the  sparks  is 
again  a  maximum ;  then  we  have,  on  the  preceding  theory, 
V'/V=l'/l.  Blondlot  found,  as  the  result  of  a  large  number  of 
experiments,  that  I'  is  equal  to  I ;  hence  he  concludes  that  the 
velocity  of  propagation  of  Rontgen  rays  through  the  air  is  equal 
to  the  velocity  of  propagation  of  an  electrical  disturbance  along 
a  metal  wire,  and  this  is  known  to  be  equal  to  the  velocity  of 
light ;  so  that  he  regards  the  experiments  as  proving  that  the 
velocity  of  Rontgen  rays  is  the  same  as_ that  of  light. 

I  do  not  see  how  Blondlot's  explanation  of  the  effects  could 
apply  unless  the  effects  produced  by  the  rays  on  the  spark  gap 
ceased  simultaneously  with  the  rays,  and  if  this  effect  is  due  to 
the  ionisation  of  the  gas  round  the  air  gap  we  should  expect 
the  effect  to  last  some  time  after  the  rays  cease. 

311.  Diffraction  of  Rontgen  Rays.  Many  experiments  have 
been  made  to  test  whether,  as  in  the  case  of  light,  there  are 
both  inside  and  outside  the  boundary  of  the  shadows  cast  by 
very  small  objects,  variations  in  the  intensity  of  the  rays  corre- 
sponding to  the  well-known  diffraction  fringes.  Rontgen*,  who 
investigated  this  point,  was  never  able  to  satisfy  himself  that 
the  effects  he  obtained  were  undoubtedly  due  to  diffraction. 
Fommf  observed  in  the  photograph  of  a  narrow  slit  light  and 
dark  bands  which  looked  like  diffraction  bands,  but  observations 
with  different  sized  slits  showed  that  this  could  not  be  their 
origin,  and  Haga  and  WindJ  have  explained  them  as  contrast 
effects.  These  observers,  who  have  made  long-continued  re- 
searches on  this  subject,  have  obtained  with  a  narrow  V-shaped 
slit,  only  a  few  thousandths  of  a  millimetre  broad  at  its  widest 
point  and  made  of  platinum  plates  about  half  a  millimetre  thick, 
effects  which  would  be  produced  by  diffraction,  and  which  have 
not  been  explained  in  any  other  way.  The  image  of  such  a  slit 
is  shown  on  a  greatly  magnified  scale  in  Fig.  178  §:  this  diagram 

*  Bontgen,  Wied.  Ann.  Ixiv.  p.  18,  1898. 

t  Fomm,  Wied.  Ann.  lix.  p.  350,  1896. 

$  Haga  and  Wind,  Wied.  Ann.  Ixviii.  p.  884,  1899. 

§  Wind,  Physikalische  Zeitschrift,  ii.  p.  292,  1901. 


312]  RONTGEN   RAYS.  529 

represents  one  of  the  photographs  with  its  vertical  dimensions 
magnified  two  hundred  times,  while  the  horizontal  dimensions  are 


Fig.  178. 

only  doubled.  The  broadening  of  the  narrow  part  of  the  shadow 
is  the  effect  relied  upon  for  showing  the  diffraction.  To  obtain 
a  similar  amount  of  broadening  with  light  of  a  definite  wave 
length,  the  length  of  the  wave  would  have  to  be  of  the  order 
2  x  10~8  cm.  If  we  regard  the  Rontgen  rays  as  due  to  discon- 
tinuous pulses,  this  will  be  the  order  of  the  thickness  of  the 
pulse  for  the  particular  rays  under  consideration. 

312.  We  have  no  evidence  that  the  Rontgen  rays  suffer  any 
deflection  when  passing  through  magnetic  fields  strong  enough  to 
produce  very  large  deflections  of  cathode  rays. 


T.  G.  34 


CHAPTER  XIX. 

PROPERTIES   OF  MOVING  ELECTRIFIED   BODIES. 

313.  As  Rontgen  rays  are  produced  when  the  cathode  rays 
strike  against  an  obstacle,  and  as  the  cathode  rays  consist  of 
negatively  charged  particles,  it  is  of  interest  to  examine  the 
effects  which  are  produced  when  the  motion  of  a  charged  particle 
is  suddenly  stopped. 

When   a   particle   with  a  charge   e  of  electricity  is   moving 

uniformly  parallel  to  the  axis  of  z  with  a  velocity  w,  it  produces 

at  a  point  whose  coordinates  relative  to  the  particle  are  x,  y,  z,  a 
radial  electric  polarization  equal  to 

a?  +  y2  4-  z'2  U 


4ir(F*-ii#./  ,    •    2a_      Fa        V 
\f  +  y  '\V*=&*}\ 

and  a  magnetic  force  whose  components  a,  /3,  y  parallel  to  the 
axes  of  a?,  y,  z  respectively  are  given  by  the  equations 

TT- 


Vw 

a  =  — 


7  =  0, 

V  being  the  velocity  of  propagation  of  electrodynamic  dis- 
turbances through  the  medium  surrounding  the  sphere  (see 
Recent  Researches  in  Electricity  and  Magnetism,  pp.  18  —  19). 


314]  PROPERTIES  OF  MOVING   ELECTRIFIED   BODIES.  531 

When  w  the  velocity  with  which  the  particle  is  moving  is  small 
compared  with  V,  the  radial  electric  polarization  becomes 

e  1 

the  same  as  when  the  particle  is  at  rest ;  and  the  components  of 

the  magnetic  force  are  given  by 

11 


y 
—  —  ew  y 


x 


7  =  0. 

314.  In  an  electric  field  in  which  the  components  of  the  electric 
polarization  are  f,  g,  h,  those  of  the  magnetic  induction  a,  b,  c, 
there  is  mechanical  momentum,  the  components  U,  V,  W  of 
which  per  unit  volume  are  given  by  the  equations 

U=cg-bh, 
V=ah-cf, 
W=bf-ag 
(see  Recent  Researches,  p.  13). 

Substituting  the  expressions  we  have  given  for  the  polarization 
and  magnetic  force  due  to  the  moving  charged  particle  and  in- 
tegrating throughout  the  space  outside  a  small  sphere  of  radius  a 
described  round  the  electrified  point  we  find  if  P,  Q,  R  are  the 
components  of  the  resultant  momentum  of  the  medium  outside 
the  sphere  in  this  direction 


.........  (i), 

where  p  is  the  magnetic  permeability  of  the  medium  and 


sin  ^  —  -T7- 


(see  Recent  Researches,  p.  21) ;  when  w  is  small  compared  with  V, 
the  value  of  R  reduces  to 

2  ue2 


34—2 


532  PROPERTIES  OF  MOVING   ELECTRIFIED  BODIES.  [315 

Thus  if  m  is  the  mass  of  the  particle  the  momentum  due  to 
its  motion  is  not  m'w  but  in  virtue  of  the  momentum  in  the 
electromagnetic  field 

m'w  4-  R, 
or  when  w  is  small 


a 
Thus  the  particle  will  in  this  case  behave  as  if  its  mass  were 

,  ,      2yue2 
increased  by  -  —  . 

315.  In  the  general  case  when  w  is  not  small,  let  %  denote 
m'w  +  R  and  suppose  the  particle  is  acted  on  by  'a  magnetic  force 
H  at  right  angles  to  its  direction  of  motion,  the  mechanical  force 
acting  upon  the  particle  is  Hew,  hence  if  in  the  time  Bt  the 
direction  of  motion  is  deflected  through  an  angle  &6  we  have 


if  8s  be  an  element  of  the  path,  p  its  radius  of  curvature,  then 

~a     Ss     wSt 
ou  —  —  =  ------  , 

P        P 
hence  p  =  ~-  ; 

but  if  elm  is  the  ratio  of  the  charge  to  the  effective  mass  then 

mw 
^He* 

hence  m  =  ^  =  m'  H  —  . 

w  w 

Now  from  the  expression  (1)  for  R  we  see  that  when  w 
approaches  F,  R/w  increases  rapidly,  hence  if  what  we  may  call 
the  electrical  mass  is  comparable  with  the  mechanical,  we  should 
expect  m/e  would  vary  with  the  velocity  of  the  particle,  increasing 
as  the  velocity  increases.  From  the  expression  given  for  R  we 
see  that  it  is  only  with  particles  moving  with  velocities  com- 
parable with  that  of  light  that  we  could  expect  to  get  measurable 
variations  in  the  value  of  m/e  ;  happily  particles  travelling  with 
these  speeds  are  furnished  by  radium  and  the  value  of  m/e 
for  these  rapidly  moving  molecules  has  been  made  the  subject  of 
a  most  interesting  research  by  Kaufmann*. 

*  Kaufmann,  Gottingen  Nach.,  Nov.  8,  1901. 


316]  PROPERTIES   OF   MOVING  ELECTRIFIED   BODIES.  533 

316.    The  method  used  by  Kaufmann  is  illustrated  in  Fig.  179. 


Fig.  179. 

A  small  piece  of  radium  was  placed  at  C  in  a  vessel  from 
which  the  air  was  extracted,  the  radiations  from  the  radium  passed 
through  a  strong  electric  field  in  the  space  between  the  parallel 
plates  Pl}  P2  which  were  '1525  cm.  apart  and  maintained  at  a 
potential  difference  of  6750  volts,  they  then  passed  through  a 
small  hole  D  in  a  diaphragm  and  then  on  to  a  photographic 
plate  E\  during  the  whole  of  their  journey  from  C  to  E  the  rays 
were  under  the  influence  of  a  magnetic  field  produced  by  the 
electromagnet  NS ;  the  deflection  due  to  the  magnetic  field  was 
at  right  angles  to  that  due  to  the  electric.  If  the  electric  and 
magnetic  fields  were  not  in  action  all  the  rays  from  the  radium 
would  strike  the  photographic  plate  at  the  same  point,  when 
however  the  rays  are  exposed  to  the  electric  and  magnetic  fields 
the  deflection  will  depend  upon  the  velocity,  so  that  the  rays  of 
different  velocities  will  now  strike  the  plate  at  different  points 
and  the  impression  produced  by  the  radium  on  a  plate  will  be  a 
curved  line ;  by  measuring  the  photograph  the-deflection  due  to  the 
magnetic  field  and  also  that  due  to  the  electric  field  can  be  found, 
and  from  these  deflections  (see  Chap.  V.)  the  values  of  v  the  velocity 
of  the  particles  and  the  corresponding  value  of  e/m  can  be  found. 
Kaufmann  found  that  when  his  plates  were  exposed  for  several 


534 


PROPERTIES   OF  MOVING   ELECTRIFIED   BODIES. 


[316 


days  he  got  a  clearly  defined  curve  from  which  he  deduced  the 
following  values  of  e/m  and  v. 


v  x  10-10 

e/m  x  10~7 

2-83 

•63 

2-72 

•77    ' 

2-59 

•975 

2-48 

1-17 

2-36 

1-31 

It  is  clear  from  these  numbers  that  e/m  diminishes  as  the 
velocity  of  the  particle  increases,  so  that  if  e  remains  the  same 
the  value  of  ra  increases  with  the  velocity.  As  this  increase  must 
be  due  to  the  '  electrical  mass '  it  follows  that  the  electrical  mass 
must  be  comparable  with  the  mechanical  mass.  To  find  the 
proportion  between  the  two,  we  must  make  some  assumption  as 
to  the  distribution  of  electricity  on  the  corpuscle.  Kaufmann 
assumed  that  the  distribution  was  the  same  as  if  the  corpuscle 
were  a  conducting  sphere ;  the  electrical  field  due  to  a  moving 
conducting  sphere  has  been  solved  in  great  detail  by  Searle*. 
On  this  supposition  Kaufmann  calculated  from  his  experiments 
that  the  electrical  mass  of  a  slowly  moving  corpuscle  was  about  J 
of  the  mechanical  mass.  He  points  out  that  the  proportion  will 
depend  upon  the  assumption  made  as  to  the  distribution  of 
electricity  over  the  corpuscle,  and  in  a  later  paper  he  shows  that 
his  experiments  are  consistent  with  the  view  that  the  whole  of  the 
mass  is  electrical. 

There  does  not  seem  to  me  any  reason  for  attributing  electrical 
conductivity  to  the  corpuscle  itself,  and  I  prefer  to  take  another 
view  of  the  electric  field  due  to  a  corpuscle  and  to  assume  that  it 
coincides  with  that  part  of  the  field  due  to  a  point  charge  which 
is  outside  a  small  sphere  of  radius  a  having  the  point  charge  for 
centre.  On  this  supposition  the  electrical  mass  is  R/w  where  R 
is  given  by  equation  (1).  Using  this  formula  I  have  calculated, 
on  the  supposition  that  the  whole  of  the  mass  is  electrical,  the 
ratios  of  the  masses  of  the  corpuscles  moving  with  the  velocities 
occurring  in  Kaufmann's  experiments  to  the  mass  of.  a  corpuscle 


Searle,  Phil.  Mag.  v.  44,  p.  340,  1897. 


317] 


PROPERTIES   OF   MOVING   ELECTRIFIED   BODIES. 


535 


moving  with  an  exceedingly  small  velocity;  the  values  of  this 
ratio  (p)  are  given  in  the  following  table,  p  are  the  values  ob- 
served by  Kaufmann. 


1 

v  x  10-10 

p' 

P 

2-85 

3-1 

3-09 

2-72 

2-42 

2-43 

2-59 

2-0 

2-04 

2-48 

1-66 

1-83 

2-36 

1-5 

1-65 

Thus  the  observed  and  calculated  values  of  p  do  not  differ 
by  more  than  10  per  cent.,  suggesting  that  all  the  mass  of  the 
corpuscles  is  electrical  in  its  origin.  On  this  supposition  the  mass 

of  a  slowly  moving  corpuscle  is  -  — -or  m/e  =  -r  pe/a,  from  the 

o   a  o 

known  values  of  m/e  and  e  we  find  a  to  be  about  10~13  cm.  As 
the  mass  of  a  corpuscle  has  been  seen  to  have  an  electrical  origin 
the  question  naturally  suggests  itself  whether  the  masses  of  all 
bodies  may  not  have  the  same  origin. 

317.  The  phenomena  we  have  described  in  the  earlier  part  of 
the  book  show  that  corpuscles  are  a  constituent  of  all  bodies,  so  that 
part  of  the  mass  of  these  bodies  is  due  to  the  corpuscles  and  is 
therefore  electrical :  it  is  easy  to  imagine  a  form  of  atom  for  which 
the  whole  mass  would  be  electrical.  For  suppose  that  the  atoms 
are  made  up  of  a  large  number  of  negatively  electrified  corpuscles 
each  corpuscle  being  associated  with  its  corresponding  positive 
charge,  and  suppose  that  these  positive  charges  are  spread  over  a 
much  greater  volume  than  the  corpuscles,  the  aggregation  thus 
formed  would  consist  of  a  distribution  of  positive  electricity  through 
a  sphere,  the  corpuscles  being  distributed  through  the  sphere  in 
such  a  way  as  to  be  in  equilibrium  under  their  own  repulsions 
and  the  attractive  force  to  the  centre  of  the  sphere  arising  from 
the  positive  electrification,  in  fact  we  should  get  an  atom  similar 
to  that  described  by  Lord  Kelvin  in  his  paper  "^Epinus  Atomized" 
(Phil.  Mag.  Mar.  1902).  If  the  radius  of  the  sphere  occupied  by 
the  positive  electrification  is  large  compared  with  the  radius  of  a 
corpuscle,  it  'is  easy  to  show  that  the  mass  of  the  atom  will  only 
differ  slightly  from  the  sum  of  the  masses  of  the  individual 


536  PROPERTIES   OF   MOVING   ELECTRIFIED   BODIES.  [318 

corpuscles  considered  as  discrete  systems.  Thus  in  any  aggrega- 
tion or  dissociation  of  a  system  of  atoms  the  changes  in  the  mass 
would,  since  the  number  of  corpuscles  remains  unaltered,  be 
exceedingly  small  in  comparison  with  the  whole  mass  of  the 
atoms  in  any  particular  state. 

318.  There  is  another  point  of  view  from  which  we  may  regard 
the  question  of  electrical  mass  which  may  perhaps  be  most  easily 
explained  by  considering  the  simple  case  of  a  moving  charged 
particle.  If  a,  b,  c  are  the  components  of  the  magnetic  in- 
duction, /,  g,  h  those  of  the  polarization,  i.e.  the  number  of 
Faraday  tubes  passing  through  unit  area  at  right  angles  to  their 
length,  then  (see  Recent  Researches,  p.  13)  the  components  of 
the  momentum  in  the  field  are 

eg  —  bh,         ah  —  cf,         bf—  ag. 

The  magnetic  field  is  due  to  the  motion  of  the  Faraday  tubes, 
and  if  the  charged  point  is  moving  parallel  to  the  axis  of  z 
with  a  velocity  w  we  have  (see  Recent  Researches,  p.  8) 

a  =  —  4i7r^wg, 

b  =  4>7TfJLWf, 

c  =  0, 

where  p  is  the  magnetic  permeability  of  the  medium  through 
which  the  Faraday  tubes  are  moving.  Substituting  these  values 
for  a,  b,  c  in  the  expressions  for  the  components  of  the  momentum 
we  find  that  these  become 

-  4,-jr/jLwfh,         —  ^-jriJLwgh,         4>7r/ji  (/2  +  (f  +  h-)  w  —  4  TT^W. 
Thus  the  resultant  momentum  is  at  right  angles  to  the  direction 
of  the  Faraday  tube  and  is  in  the  plane  through  the  tube  and  the 
direction  of  motion  of  the  particle,  the  magnitude  of  the  resultant 
momentum  is 

4,7TfjL  (/2  +  g2  +  A2)  w  sin  6, 

where  6  is  the  angle  between  the  Faraday  tube  and  its  direction 
of  motion,  thus  w  sin  0  is  the  velocity  of  the  tube  at  right  angles 
to  its  length.  Hence  we  see  that  the  momentum  in  the  field  is 
the  same  as  would  exist  if  the  Faraday  tubes  carry  with  them  when 
they  move  at  right  angles  to  themselves  a  mass  of  the  ether  equal 
per  unit  volume  to  47r//,  (/2  +  #2  +  A2),  while  when  the  tubes  move 
parallel  to  their  length  they  do  not  drag  any  ether  along  with 


319]  PROPERTIES  OF   MOVING  ELECTRIFIED   BODIES.  537 

them.  The  momentum  in  the  field  is  the  momentum  of  this 
bound  ether.  Thus  on  this  view  the  electrical  mass  of  a  charged 
body  represents  the  mass  of  the  ether  dragged  along  or  imprisoned 
by  the  Faraday  tubes  associated  \vith  that  body,  and  thus  on  the 
hypothesis  mentioned  above  that  all  mass  is  electrical  in  its  origin 
it  would  follow  that  the  mass  of  all  bodies  has  its  origin  in  the 
ether  dragged  along  by  the  Faraday  tubes  associated  with  the 
body  (see  Proceedings  of  Cambridge  Philosophical  Society,  Mar. 
1903);  the  author  hopes  shortly  to  publish  a  more  detailed  account 
of  the  consequences  which  result  from  this  point  of  view. 

Effect  of  suddenly  stopping  a  moving  charged  particle. 

319.  The  author  gave  an  analytical  investigation  of  this 
question  in  the  Philosophical  Magazine  for  Feb.  1897  ;  the  follow- 
ing geometrical  treatment  of  the  same  problem  is  based  upon  the 
method  of  Faraday  tubes.  Let  us  consider  the  case  of  a  charged 
point  moving  so  slowly  that  the  Faraday  tubes  are  uniformly 
distributed,  and  suppose  the  point  to  be  suddenly  stopped,  the 
effect  of  stopping  the  point  will  be  that  a  pulse  travels  outwards 
from  it  with  the  velocity  V,  but  as  the  Faraday  tubes  have  inertia 
they  will  until  the  pulse  reaches  them  go  on  moving  uniformly 


Fig.  180. 

with  a  velocity  w  parallel  to  the  axis  of  z,  i.e.  they  will  continue 
in  the  same  state  of  motion  as  before  the  stoppage  of  the  point. 


538  PROPERTIES  OF  MOVING   ELECTRIFIED   BODIES.  [319 

Let  us  consider  the  behaviour  of  a  tube  which  at  the  moment  of 
stopping  the  charge  had  the  position  PQ,  and  consider  the  state 
of  things  after  an  interval  t  from  the  stoppage ;  a  pulse  whose 
thickness  S  depends  on  the  time  taken  to  stop  the  particle  will 
have  travelled  out  to  a  distance  Vt.  In  front  of  this  pulse  the 
motion  of  the  tubes  will  not  have  been  affected,  i.e.  they  have 
travelled  parallel  to  themselves  through  a  distance  wt  parallel  to 
the  axis  of  z ;  behind  the  pulse  the  tube  will  have  been  brought 
to  rest  along  the  line  it  occupied  when  the  point  was  stopped, 
thus  the  portions  behind  and  in  front  of  the  pulse  will  be  repre- 
sented by  ON,  P'Q'  in  Fig.  180.  Hence  to  preserve  the  continuity 


0  I0*t  0  0  0'  0"  0'" 

Fig.  181. 

of  the  tube  it  must  bend  sharply  round  in  the  pulse  itself,  so  that 
now  the  tube  has  a  considerable  tangential  component.  The 
stoppage  of  the  point  will  thus  produce  a  tangential  component 
in  the  electric  force  which  we  proceed  to  calculate,  supposing  that 
the  pulse  is  very  thin  so  that  the  tube  in  it  may  be  regarded  as 
approximately  straight.  Then 

tangential  electric  polarization     P'N     wsindt 
normal  electric  polarization        NN'  8 

where  t  is  the  time  which  has  elapsed  since  the  stoppage  of  the 
particle  and  S  is  the  thickness  of  the  pulse. 

The  left-hand  diagram  in  Fig.  181  shows  the  configuration  of 
the  tube  at  the  times  when,  if  the  particle  had  not  been  stopped, 
it  would  have  been  at  o,  o",  o". 

Since  the  normal  electric  polarization  at  a  distance  r  from  the 


319]  PROPERTIES   OF   MOVING   ELECTRIFIED   BODIES.  539 

particle  is  equal  to  e/4>7rr2  and  if  V  is  the  velocity  of  propagation 
of  the  disturbance  Vt  =  r,  we  have  from  (1) 


.  •  i    i    4.  •        1-4.-  e 

tangential  electric  polarization  =  .  -  —  ^   —  = 

as  this  electric  polarization  is  moving  at  right  angles  to  itself 
with  a  velocity  V  it  produces  a  magnetic  force  at  right  angles 
to  the  polarization  and  to  its  direction  of  motion,  i.e.  parallel  to, 
but  in  the  opposite  direction  to  the  magnetic  force  before  the 
particle  was  stopped  and  equal  to  4<7rV  times  the  polarization, 

a 

i.e.  to     .,  w  sin  6  ;   hence  in  the  pulse   we   have  (1)  a  tangential 

electric  polarization  equal  to  ew  sin  #/47rrSF,  and  (2)  a  magnetic 
force  equal  to  ew  sin  0/rS  ;  as  these  only  vary  inversely  as  the 
distance  from  the  particle  while  the  polarization  and  magnetic 
force  before  the  particle  was  stopped  varied  inversely  as  the 
square  of  the  distance,  their  magnitudes  in  the  pulse  will  except 
in  the  immediate  neighbourhood  of  the  particle  be  very  great 
compared  with  their  values  outside  the  pulse.  Thus  the  stoppage 
of  the  charged  particle  is  accompanied  by  the  propagation  out- 
wards of  a  thin  pulse  of  very  intense  electric  and  magnetic  force  ; 
pulses  produced  in  this  way  constitute  I  believe  the  Rb'ntgen 
rays.  It  will  be  seen  that  on  the  Electromagnetic  Theory  of 
Light  the  pulses  which  we  suppose  to  constitute  the  Rontgen 
rays  are  in  many  respects  identical  with  waves  of  visible  light  ; 
both  consist  of  electric  and  magnetic  forces  at  right  angles  to 
each  other  and  to  the  direction  of  propagation  ;  the  difference 
between  the  Rontgen  rays  and  a  beam  of  sodium  light  is  that 
the  thickness  of  the  Rontgen  ray  pulse  is  very  small  compared 
with  the  wave-length  of  sodium  light,  and  that  in  the  Rontgen 
rays  there  is  not  that  regular  periodic  character  occurring  in  a 
train  of  waves  of  constant  wave-length.  Sir  George  Stoker  in 
the  Wilde  Lecture  given  before  the  Manchester  Philosophical 
Society  showed  that  many  of  the  differences  between  Rontgen 
rays  and  ordinary  light,  such  for  example  as  the  absence  of 
refraction,  could  be  explained  by  the  theory  that  the  Rontgen 
rays  consisted  of  pulses  whose  thickness  was  very  small  compared 
with  the  wave-length  of  visible  light. 

A  very  complete  investigation  of  the  diffraction  of  Rontgen 
rays  from  this  point  of  view  has  been  given  by  Sommerfeld*. 
*  Sommerfeld,  Phyrik.  Zeit.  (1)  p.  105,  (2)  p.  55,  1900. 


540 


PROPERTIES   OF   MOVING   ELECTRIFIED   BODIES. 


[320 


320.    If  H  is  the  magnetic  force  in  the  pulse  the  energy  per  unit 
volume  of  the  pulse  is  -—-  H2  (half  of  this  is  due  to  the  magnetic 

and  half  to  the  electric  field),  substituting  the  value  given  for  H 
and  integrating  throughout  the  volume  of  the  pulse  we  find  that 
the  energy  in  the  pulse  is 


3 

Thus  the  amount  of  energy  radiated  away  in  the  pulse  varies 
inversely  as  the  thickness  of  the  pulse,  and  the  thickness  of  the 
pulse  depends  upon  the  abruptness  with  which  the  particle  is 
stopped  ;  if  the  stoppage  is  very  abrupt  the  pulse,  is  thin,  if  it  is 
gradual  it  is  wide.  The  amount  of  energy  radiated  away  in 
Rontgen  rays  bears  to  the  energy  in  the  field  the  ratio  of  2a 
to  8,  where  a  is  the  radius  of  the  corpuscle  ;  see  p.  532.  If  8  is 
equal  to  2a  then  all  the  energy  (assuming  that  the  mass  of  the 
particle  arises  wholly  from  electrical  causes)  will  be  radiated  away; 
with  thicker  pulses  only  a  portion  of  the  energy  is  radiated,  the  rest 
is  absorbed  where  the  particle  is  stopped. 

321.  In  the  preceding  investigation  we  have  supposed  that 
the  velocity  of  the  particle  is  small  compared  with  the  velocity  of 
light,  the  same  method  will  however  apply  when  this  limitation 
is  removed. 


When  the  particle  moves  with  the  velocity  of  light  the  electric 
and  magnetic  forces  before  the  stoppage  are  confined  to  a  plane 
through  the  centre  of  the  sphere  at  right  angles  to  its  direction  of 
motion.  To  find  the  effect  at  a  time  t  after  the  stoppage  of  such  a 


322]  PROPERTIES  OF   MOVING   ELECTRIFIED   BODIES.  541 

particle  we  apply  the  same  principle  as  before,  that  outside  a  pulse 
whose  radius  is  Vt  the  field  is  the  same  as  if  the  particle  had  gone 
on  moving  uniformly  with  the  velocity  it  had  when  stopped,  and 
that  between  the  charged  particle  and  the  pulse  the  distribution 
of  Faraday  tubes  is  uniform.  Thus  we  shall  find  a  deformation 
of  the  Faraday  tubes  such  as  is  shown  in  Fig.  183 ;  the  plane  of 
magnetic  and  electric  force  travels  on  as  if  the  particle  had  not 
been  stopped,  since  it  always  keeps  just  outside  the  sphere  of 
radius  Vt  and  there  is  in  addition  a  spherical  pulse  formed  by 
the  parts  joining  the  Faraday  tubes  inside  the  sphere  to  those 
outside. 


Q 


Fig.  183. 

322.  To  find  the  magnitude  of  the  tangential  polarization  T 
we  may  proceed  as  follows.  Consider  an  element  of  the  pulse 
ABCDEFGH  formed  by  the  intersection  of  two  meridian  planes 
ABFE,  DCGH  inclined  at  an  angle  $$  and  two  cones  BCGF, 
ADHE  whose  semi-vertical  angles  are  0  and  0  +  dO  with  the 
outer  and  inner  spheres  bounding  the  pulse,  then  since  there 
is  no  free  electricity  inside  this  element  the  number  of  lines 
of  force  which  leave  the  face  BCGF  must  equal  the  sum  of  the 
numbers  entering  the  faces  AD  EH  and  EFGH,  hence  if  8  is  the 
thickness  of  the  pulse,  T  the  tangential  polarization,  we  have 

~  (TSr  sin  0  d<f>)  dO  =  -*-  2  rdO  r  sin  6  d<f>, 

du 


or  ~<TSrsin<9)  =  .-  sin 

CiU  47T 


542  PROPERTIES   OF  MOVING   ELECTRIFIED   BODIES.  [323 

*  ~  CQS  0 


T- 

~ 


sin  6 

and  H  the  magnetic  force  in  the  spherical  pulse  is  given  by  the 
equation 

„._  eV\  —  cos  6 
=  rB  ""sin  6     ' 

Magnetic  and  Electric  Forces  due  to  the  acceleration  of 
charged  particles. 

323.  In  the  investigation  in  Art.  319  we  supposed  that  the 
particle  was  reduced  to  rest ;  exactly  the  same  method  will  however 
give  us  the  effects  produced  when  smaller  changes  in  the  velocity 
of  the  particle  occur  and  when  the  velocity  of  the  particle  is  altered 
without  being  destroyed.  We  saw  in  Art.  319  that  when  a 
particle  moving  with  a  velocity  w  is  reduced  to  rest,  i.e.  when 
a  change  w  is  produced  in  the  velocity,  a  tangential  electric 
polarization  T  and  a  tangential  magnetic  force  H  are  produced 
which,  at  a  distance  r  from  the  particle,  are  at  the  time  r/  V  after 
stopping  the  particle  given  by  the  equations 

„  _  ew  sin  6      „  _  ew  sin  0 

J-  —    .  — tTV>  i     -tl  — s \ 


if  r  is  the  time  taken  to  stop  the  particle,  8  (the  thickness  of  the 
pulse)  is  equal  to  FT,  hence  we  may  write 

~  _  ew  sin  6      Tr_ew  sin  6 
^4VFVT'    '  rVr 

If  now  the  velocity  of  the  particle  instead  of  being  diminished 
by  w  in  the  time  r  is  increased  by  &w  in  the  same  time,  we  can 
prove  by  exactly  the  same  method  that  there  will  be  a  tangential 
electric  polarization  T'  and  a  magnetic  force  H'  given  by  the 
equations 

m,  _     e&w  sin  6      rr>  _     eBw  sin  6 
"  '    ' 


rVr    "' 

since  &w  is  the  increase  in  the  velocity  in  the  time  T,  Sw=fr, 
where  /is  the  acceleration  of  the  particle;  hence  substituting  this 
value  for  Sw,  we  have 

y,  =     e/sin  d      jy,=  _e/sm0 
4?r7V  '  rV     ' 


324]  PROPERTIES  OF   MOVING   ELECTRIFIED  BODIES.  543 

thus  an  accelerated  charged  particle  produces  in  the  surrounding 
field  tangential,  magnetic,  and  electric  forces  which  vary  inversely 
as  the  distance  from  the  particle. 

By  Poynting's  theorem  the  rate  at  which  energy  is  flowing 
radially  through  unit  area  of  surface  is  V*T'H'\  integrating  this 
expression  over  the  surface  of  a  sphere  having  its  centre  at  the 
particle,  we  find  that  the  rate  at  which  energy  crosses  the  surface 

2  e2/"2 
is  -   Jy  ,  a  result  given  by  Larmor  (Phil.  Mag.  v.  44,  p.  503,  1897). 

324.  The  radiation  of  energy  from  the  moving  charged  particle 
will  modify  its  motion;  thus  supposing  the  particle  to  have  the 
mass  m  and  to  be  acted  upon  by  a  uniform  force  X,  then  if  v  is  the 
velocity  of  the  particle  the  kinetic  energy  is  ^mv2  and  the  accele- 


CM  t) 

ration  is  -r  ;  suppose  that  in  time  $t  the  particle  moves  over  a 
ctt 

distance  S#,  the  work  done  on  the  particle  by  the  external  force 
is  XeBx,  this  work  must  equal  the  increase  in  the  kinetic  energy 
plus  the  energy  radiated  away  in  time  St,  hence 

v  *       */i      ox     2  e* 
Xetx  =  3  (Jrnt?2)  +  g  y 

dv     2  e2    dv 


we  see  from  this  equation  that  if  the  particle  starts  from  rest  its 
acceleration  is  initially  zero  instead  of  Xejm. 


Solving  equation  (1),  we  find 

mdv 
Xe 


(2). 


Thus  if  T  is  the  time  required  for  the  acceleration  to  reach  half 
its  final  value  Xe/m,  we  have 


Thus,  until  a  time  comparable  with  ez/Vm  has  elapsed,  the 
acceleration  of  th$  particle  and  therefore  the  rate  at  which  it  is 
losing  energy  by  radiation  will  be  small  compared  with  their 


544  PROPERTIES  OF  MOVING   ELECTRIFIED   BODIES.  [324 

final  values  ;  thus  if  a  pulse  of  electric  force  passes  over  a  charged 
particle  a  much  smaller  proportion  of  the  energy  in  the  pulse 
will  be  radiated  away  if  the  pulse  is  so  thin  that  the  time  taken 
for  it  to  pass  over  the  particle  is  comparable  with  T  than  will  be 
radiated  from  the  thick  pulses  whose  time  of  transit  is  much 
longer,  for  then  the  thin  pulses  will  have  much  greater  penetrating 
power  than  the  thick  ones.  The  expression  given  in  Art.  138  for 
the  coefficient  of  absorption  of  a  Kontgen  ray  only  applies  to  the 
case  when  the  pulse  is  so  thick  that  the  time  taken  for  it  to  pass 
over  a  charged  particle  is  large  compared  with  e2/m  V,  the  coefficient 
of  absorption  for  thinner  pulses  is  much  smaller. 


SUPPLEMENTARY  NOTES. 


CHAPTER  I. 

EXPERIMENTS  made  by  McClemian  (American  Physical  Society,  Dec. 
1902),  Rutherford  and  Cooke  (ibid.),  Sfcrutt  (Nature,  Feb.  19,  1903) 
have  shown  that  the  leak  through  air  in  a  closed  vessel  depends  upon 
the  material  of  which  the  walls  of  the  vessel  are  made;  the  variations 
with  different  substances  are  very  considerable,  thus  Strutt  found  that 
with  one  specimen  of  platinum  for  the  walls  of  the  vessel,  the  current 
through  the  vessel  was  three  times  that  when  the  walls  were  made  of 
glass.  This  shows  that  part  of  the  ionisation  is  due  to  radiation  given 
out  by  the  walls.  The  same  conclusion  had  previously  been  arrived  at 
by  Patterson  (Proc.  Camb.  Phil  Soc.  xn.  p.  44);  as  the  result  of  his 
experiments  on  the  variation  of  the  current  through  a  large  vessel  with 
the  pressure :  he  found  that  starting  from  atmospheric  pressure  the  first 
diminution  of  pressure  produced  little  or  no  effect  upon  the  leak,  it  was 
not  until  the  pressure  had  been  considerably  reduced  that  diminution  in 
pressure  produced  a  proportionate  diminution  in  the  rate  of  leak,  this  is 
precisely  what  would  occur  if  the  ionisation  were  due  to  easily  absorbed 
rays  given  out  by  the  sides  of  the  vessel  which  at  high  pressures  got 
absorbed  before  they  reached  the  opposite  sides  of  the  vessel,  for  in  this 
case  as  long  as  the  pressure  is  high  enough  to  make  the  gas  absorb  all 
the  rays  before  they  travel  across  the  vessel,  the  number  of  ions  pro- 
duced and  therefore  the  saturation  current  will  be  independent  of  the 
pressure;  when  however  the  pressure  is  reduced  so  low  that  the  rays 
given  out  by  the  walls  are  able  to  travel  across  the  vessel  without  being 
absorbed  a  diminution  of  the  pressure  will  diminish  the  ionization  and 
therefore  the  saturation  current.  Strutt  (loc.  cit.)  has  observed  similar 
effects. 

Part  of  the  ionization  in  a  closed  vessel  seems  to  be  due  to  a  veijy 
penetrating  radiation  which  traverses  the  walls  of  the  vessel,  for 
McClennan  (loc.  cit)  and  Rutherford  have  shown  that  if  the  vessel  be 
shielded  by  an  envelope  of  lead  or  a  thick  layer  of  water  the  satura- 
tion current  is  reduced  by  about  20  °/o.  We  do  not  know  yet  whether 
T.  G.  35 


546  SUPPLEMENTARY   NOTES. 

the  ionisation  due  to  these  very  penetrating  rays  is  direct]}7  due  to 
their  passage  through  the  gas  or  whether  it  arises  mainly  from  a  more 
absorbable  secondary  radiation  excited  in  the  walls  of  the  vessel  by  the 
passage  through  them  of  the  more  penetrating  rays.  Patterson's 
experiments  seem  to  point  to  the  latter  as  the  more  probable.  These 
penetrating  rays  may  possibly  come  from  the  constituent  of  the 
atmosphere  which  produces  the  induced  radio-activity  on  a  negatively- 
electrified  rod  (see  page  328).  Rutherford  has  shown  that  this  gives 
out  penetrating  rays;  the  same  substance  seems  to  be  the  origin  of  the 
radio-activity  which  C.  T.  R.  Wilson  has  observed  in  freshly  fallen 
rain,  as  the  rate  at  which  this  dies  away  is  about  the  same  as  that  on 
a  negatively  electrified  wire.  The  substance  apparently  deposits  on  the 
drops  as  they  fall  through  the  air. 

The  radiation  from  the  walls  seems  most  probably  due  to  a  trace  of 
a  very  radio-active  substance  present  in  the  material,  as  walls  made  of 
different  samples  of  the  same  substances  such  as  lead,  platinum  or  tin- 
foil give  very  different  ionisations. 

Elster  and  Geitel  (Physikalische  Zeitschrift,  in.  p.  574)  show  that  air 
absorbed  in  the  soil  possesses  very  much  greater  conductivity  than 
atmospheric  air.  It  is  shown  (p.  553)  that  water  from  deep  wells 
contains  a  radio-active  gas  very  similar  in  its  properties  to  the  emana- 
tion of  radium.  The  diffusion  of  these  gases  from  the  soil  and  water 
into  the  air  must  increase  its  conductivity;  they  cannot  however 
explain  the  conductivity  of  a  gas  shut  up  in  a  closed  vessel,  as  the 
activity  of  the  gas  derived  from  water  dies  away  to  half  its  value  in 
a  few  days.  Thus  after  the  gas  had  been  shut  up  for  a  week  or  two 
this  course  of  radio-activity  would  disappear,  and  we  must  look  to 
other  causes  to  explain  the  conductivity  of  gases  confined  in  closed 
vessels;  the  experiments  described  above  indicate  that  the  ionisation 
may  be  due  to  radiation  from  the  sides  of  the  vessel  and  to  rays  from 
outside  penetrating  the  walls. 

With  reference  to  meteorological  observations  on  the  state  of  ionisa- 
tion of  the  air  it  may  be  well  to  point  out  that  observations  on  the  rate 
of  escape  from  an  electrified  body  in  the  open  air  are  of  little  value  as 
the  current  is  not  saturated  and  the  leak  depends  upon  the  velocity  as 
well  as  upon  the  number  of  the  ions.  We  can  test  the  number  of  ions 
present  in  the  air  when  in  a  steady  state  by  drawing  it  rapidly  through 
a  tube  and  measuring  the  saturation  current  between  an  axial  wire 
and  the  tube.  To  determine  the  rate  at  which  ions  are  being  produced 
in  the  free  air  is  very  difficult,  as  to  get  the  current  saturated  we  must 
enclose  the  air  in  a  vessel  and  then  we  get  the  additional  ionisation 
due  to  the  walls  of  the  vessel. 


SUPPLEMENTARY   NOTES.  547 

CHAPTER   II. 

Since  this  work  was  in  type  M.  Langevin  has  published  in  his  re- 
markably able  thesis,  Recherches  sur  les  gaz  ionises,  University  of  Paris, 
1902,  some  very  important  investigations  on  the  law  of  the  recombina- 
tion of  ions  and  the  velocities  of  the  ions  in  the  electric  field.  He 
shows  by  a  simple  calculation  that  the  recombination  of  the  positive 
and  negative  ions  is  brought  about  by  the  approach  of  the  ions  caused 
by  the  electrical  attraction  between  them  ;  if  it  were  not  for  this 
attraction  the  rate  of  recombination  of  the  ions  would  be  ver^  small 
compared  with  that  which  actually  exists.  The  number  of  collisions 
between  the  positive  and  negative  ions  caused  by  their  mutual  attrac- 
tion can  easily  be  shown  to  equal  4?r  (k^  +  k2)  ePN,  when  kl  and  k2 
are  the  velocities  of  the  positive  and  negative  ions  under  unit  electric 
force  P  and  N  respectively,  the  number  of  positive  and  negative  ions 
in  unit  volume,  if  every  collision  resulted  in  recombination,  then  a,  the 
coefficient  of  recombination  as  defined  on  p.  15,  would  equal 

4?r  (k}  +  k.2)  e, 

only  a  fraction  of  the  collisions  will  however  result  in  recombination, 
in  the  other  cases  the  kinetic  energy  acquired  ,by  the  ions  in  their 
approach  to  each  other  will  cause  them  to  separate  again  after  collision, 
and  at  low  pressure  when  the  velocities  of  the  ions  under  electric  forces 
are  large,  this  fraction  should  be  less  than  at  high  pressures  when  the 
velocities  are  small,  if  e  is  the  fraction  of  the  number  of  collisions  which 
result  in  recombination 

a  =  47T6  (k-L  +  &2)  e. 

Langevin  determines  the  value  of  e  by  the  following  method:  if  the 
gas  between  two  parallel  metal  plates  maintained  at  a  constant 
difference  of  potential  is  exposed  to  Rontgen  rays  for  the  exceedingly 
small  time  during  which  a  single  discharge  from  an  induction  coil  lasts, 
the  ions  produced  in  the  space  between  the  plates  will  begin  to  move 
towards  the  plates,  the  positive  ions  moving  towards  the  negative  plate, 
and  the  negative  towards  the  positive  ;  as  the  ions  move  past  each  other 
some  of  them  will  recombine,  so  that  Q  the  number  of  negative  ions 
coming  up  to  the  positive  plate  will  be  less  than  Q0,  the  number  of 
negative  ions  produced  by  the  Rontgen  rays  between  the  plates,  the 
stronger  the  electric  field  between  the  plates  the  faster  will  the  ions 
move  up  to  the  plates  and  the  less  time  will  there  be  for  them  to 
recombine  and  in  consequence  the  less  the  difference  between  Q  and  Q0. 
Langevin  shows  that  if  a-  is  the  density  of  the  electricity  on  the 
electrified  plates 


35—2. 


548 


SUPPLEMENTARY    NOTES. 


From    this   expression   it   is    possible  to   calculate    c ;   the   results    of 
Langevin's  experiments  are  shown  in  the  following  table : 


Ail- 

CO, 

Pressure  in  mm. 

6 

Pressure  in  mm. 

e 

152 

o-oi 

135 

o-oi 

375 

0-06 

352 

0-13 

760 

0-27 

550 

0-27 

1550 

0-62 

758 

0-51 

2320 

0-80 

1560                 0-95 

5  aim. 

0-90 

2380                p-97 

The  effect  of  pressure  on  the  chance  of  collision  resulting  in  re- 
combination is  very  clearly  seen;  thus  at  the  pressure  of  152  mm.  only 
one  collision  in  one  hundred  results  in  recombination,  at  the  atmo- 
spheric pressure  the  number  has  increased  to  one  in  four  and  at  the 
pressure  of  5  atm.  to  nine  out  of  ten. 

From  the  equation 

tt  =  4:TT€  (kj_  +  &2)  6, 

a/e  can  be  deduced  when  c  is  known. 

The  values  got  by  Langevin,  McClung,  and  Townsend  are  in  close 
agreement,  they  are  given  in  the  following  table : 


Air... 
C02  

aje 

LANGEVIN 

Me  CLUNG 

TOWNSEND 

3200 
3400 

3384 

3492 

3400 
3500 

Method  of  determining  the  velocity  of  the  ions  under  an  electric  field. 

Langevin  has  determined  ^  and  &2  by  the  following  method ; 
suppose  the  region  between  the  parallel  plates  A£,  CD  is  exposed  for 
a  very  short  space  of  time  to  Rontgen  rays,  if  there  is  such  a  strong 
electric  field  between  the  plates  that  the  recombination  of  the  ions  can 
be  neglected,  then  if  the  field  were  kept  in  one  direction  all  the 
negative  ions  would  go  to  the  positive  plate  and  all  the  positive  ones  to 


SUPPLEMENTARY   NOTES. 


549 


the  negative  ;  if  however  the  field  were  reversed  before  all  the  ions 
got  across,  then  the  charge  received  by  a  plate  would  be  less  than  in 
the  previous  case,  the  difference  would  evidently  depend  upon  the 
velocities  of  the  ions;  if  we  make  a  series  of  measurements  of  the 
charge  received  by  the  plate  when  the  field  is  reversed  at  different 
intervals  after  the  ionisation  we  shall  evidently  have  the  means  of 
determining  k^  and  k.2. 

The  numbers  obtained  by  Langevin  by  this  method  are  at  atmo- 
spheric pressure. 


Air 

C02 

*, 

*2 

1     1           I 

420 

510 

1-22 

I 

257            270            1-05 

1 

Langevin  also  investigated  the  variation  of  the  velocity  with  the 
pressure;  as  explained  in  the  text  the  velocity  of  an  ion  should  vary 
inversely  as  the  pressure  as  long  as  the  nature  of  the  ion  does  not 
change,  as  however  the  negative  ion  at  very  low  pressures  is  the 
corpuscle,  while  at  atmospheric  pressures  it  is  the  corpuscle  attached 
to  several  molecules  of  the  gas,  we  must  as  we  reduce  the  pressure 
arrive  at  a  stage  where  the  negative  ion  begins  to  get  simpler  and 
when  therefore  the  velocity  will  increase  more  rapidly  than  the  re- 
ciprocal of  the  pressure,  this  effect  is  clearly  shown  by  the  results  of 
Langevin's  experiments,  which  are  given  in  the  following  table  : 


Negative  ions 

Positive  ions 

P 

/,-, 

pk2!76 

P 

*i 

j>*,/76 

7-5  (cm.) 

6560 

647 

7'5  (cm.) 

4430 

437 

20-0 

2204 

580 

20-0 

1634 

430 

41-5 

994 

530 

41-5 

782 

427 

76-0 

510 

510 

76-0 

420 

420 

142-0 

270 

505 

142-0 

225 

425 

The  velocities  &,  and  ks  are  under  unit  electrostatic  force,  i.e.  300 
volts  per  cm. 


550  SUPPLEMENTARY    NOTES. 

The  increase  in  the  value  of  pk^  with  diminished  pressure  for  pressures 
below  20  cm.  is  clearly  marked.  There  is  a  rise  but  a  much  smaller 
one  in  the  value  of  pkl  . 

Page  19.  McClung  has  lately  investigated  at  the  Cavendish 
Laboratory  the  effect  of  temperature  upon  a,  and  finds  that  a  increases 
rapidly  as  the  temperature  increases. 

CHAPTER  VI.,  p.  130. 

H.  A.  Wilson  has  determined  (Phil  Mag.  [6]  v.,  p.  429,  1903)  e  the 
charge  on  an  iori  as  follows  :  he  produces  a  cloud  in  the  ionised  gas, 
using  an  expansion  which  will  produce  condensation  on  the  negative 
but  not  on  the  positive  ions,  thus  all  the  drops  are  negatively  electrified; 
he  then  observes  the  rate  of  fall  of  these  drops  in  an  electric  field,  the 
electric  force  being  vertical;  if  X  is  the  value  of  the  force,  acting  so  as 
to  make  the  drop  move  upwards,  e  the  charge  on  the  drop,  and  a  its 
radius,  the  downward  force  on  the  drop  is  g^-rrd3  -  Xe\  hence  by  Stokes's 
rule  the  velocity  v  with  which  the  drop  falls  will  be  given  by  the  equal 

3ATe\  or 


thus  by  measuring  v  for  different  values  of  A"  we  can  get  a  and  e;  by 
this  method  Wilson  finds 

e=  3-1  x  10-10(c.  G.s.  electrostatic  units). 


CHAPTER  VII.,  p.  144. 

C.  T.  R.  Wilson  has  recently  shown  by  using  a  very  large  vessel  for 
the  expansion  that  the  few  nuclei  which  act  as  centres  of  condensation 
in  a  gas  not  exposed  to  external  ionising  influences  such  as  Rontgen 
rays  carry  charges  and  can,  like  those  due  to  the  Rontgen  rays,  be 
removed  by  an  electric  field.  He  shows  that  the  reason  that  the 
external  field  produced  no  effect  with  smaller  vessels  is  that  in  this 
case  the  few  ions  in  the  vessel  could  be  so  easily  removed  by  a  small 
electric  force  that  differences  of  potential  accidentally  present  in  the 
vessel  were  sufficient  to  remove  the  nuclei  without  the  help  of  an 
additional  electric  field. 


CHAPTER  VIIL,  p.  160. 

H.  A.  Wilson  has  recently  shown  that  the  presence  of  even  a  very 
small  quantity  of  hydrogen  enormously  increases  the  leak  of  negative 
electricity  from  an  incandescent  platinum  wire.  The  part  of  the  leak 


SUPPLEMENTARY   NOTES.  551 

which  depends  on  the  hydrogen  increases  less  rapidly  with  the  tem- 
perature than  the  part  independent  of  the  hydrogen,  so  that  at  very 
high  temperatures  the  latter  is  the  more  important. 


CHAPTER  XI.,  p.  255. 

The  more  recent  determinations  of  the  work  required  to  ionise 
a  molecule  indicate  a  higher  value  than  that  given  in  the  text.  Thus 
Langevin  (Recherches  sur  les  yaz  ionises)  from  the  results  of  some 
experiments  of  Townsend's  comes  to  the  conclusion  that  the  work  done 
on  the  ionic  charge  in  falling  through  a  potential  difference  of  60  volts 
is  a  superior  limit  to  the  work  required  to  ionise  a  molecule.  Stark 
(Drudes  Ann.  iv.  p.  411,  1901;  vii.  p.  421,  1902)  obtains  values 
ranging  from  20  to  50  volts  for  the  same  quantity. 

The  effect  of  temperature  on  the  ionisation  of  a  gas  by  Rontgen 
rays  has  been  lately  investigated  by  McClung  at  the  Cavendish 
Laboratory;  he  finds  as  the  result  of  experiments  made  on  gases  at 
constant  pressure  and  at  constant  density,  that  the  amount  of  ionisa- 
tion in  a  given  number  of  molecules  of  a  gas  exposed  to  Rontgen  rays 
is  independent  of  the  temperature,  and  is  not,  as  Perrin  thought,  pro- 
portional to  the  absolute  temperature.  He  finds  also  that  the  absorp- 
tion of  the  rays  by  a  given  number  of  molecules  is  independent  of  the 
temperature  of  the  molecules. 

CHAPTER   XL,  p.  258. 

The  fact  that  ionisation  obeys  the  additive  law  points  to  the  con- 
clusion that  it  is  an  atomic  property,  so  that  the  likelihood  of  an  atom 
being  ionised  will  depend  upon  the  internal  kinetic  energy  possessed 
by  the  atom ;  there  are  good  reasons  for  thinking  that  the  amount  of 
this  energy  possessed  by  an  atom  as  well  as  the  number  of  atoms 
possessing  a  given  amount  of  internal  kinetic  energy  are  to  a  very 
large  extent  independent  of  the  temperature  of  the  gas;  if  we  take  this 
view  we  can  understand  why  the  very  small  proportion  of  molecules 
ionised  does  not  increase  rapidly  with  the  temperature. 

CHAPTER  XL,  p.  260. 

Barkla  (Phil.  Mag.  [6]  v.,  p.  685,  1903)  has  made  a  very  careful 
examination  of  the  secondary  Rontgen  rays  produced  when  the 
primary  rays  pass  through  a  gas;  he  has  shown  that  when  the  primary 
rays  pass  through  different  gases  at  the  same  pressure  the  intensity  of 
the  secondary  radiation  is  proportional  to  the  density  of  the  gas.  Thus 


552  SUPPLEMENTARY   NOTES 

for  example  the  intensity  of  the  secondary  radiation  due  to  oxygen  is 
to  that  from  CO2  as  32  is  to  44.  He  finds  too  that  the  penetrating 
power  of  secondary  radiation  differs  little,  if  at  all,  from  that  of  the 
primary,  so  that  the  effect  produced  by  the  gas  may  be  described  as 
a  scattering  of  the  primary  rays.  Langevin  (Recherches  sur  les  gaz 
ionises)  has  investigated  the  secondary  radiation  produced  when  the 
primary  rays  fall  upon  a  metallic  surface,  and  has  shown  that  the 
denser  the  metal  the  smaller  the  penetration  of  the  secondary  rays, 
and  also  that  the  penetrating  power  of  the  secondary  rays  increases 
with  that  of  the  primary. 

CHAPTER  XII.,  p.  290. 

Rutherford  and  Soddy  (Phil.  Mag.  [6]  v.,  p.  576,  1903)  give  strong 
reasons  for  supposing  that  radio-activity  is  the  result  of  the  breaking 
up  of  the  atom;  thus  the  radium  atom  breaks  up  at  first  into  the 
positively  electrified  particles  which  constitute  the  a  rays,  the  emana- 
tion, and  possibly  other  substances;  the  emanation  breaks  up  one  of 
the  products,  being  the  substance  which  gives  rise  to  induced  radio- 
activity, this,  as  it  is  radio-active,  breaks  down  again  into  products 
which,  since  they  are  not  radio-active,  have  not  been  detected. 

W.  B.  Hardy  has  recently  shown  that  the  rays  from  radium  as  well 
as  Eontgen  rays  produced  very  marked  reddish-brown  coloration  in 
a  solution  of  iodoform  in  chloroform. 


CHAPTER  XII.,  p.  302. 

A  very  interesting  account  of  the  properties  of  radium  will  be 
found  in  the  theses  entitled  Recherches  sur  les  substances  radio-actives, 
lately  published  by  Mme.  Curie. 

Mme.  Curie  and  Laborde  have  recently  shown  (Comptes  Rendus, 
Mar.  16,  1903)  that  the  salts  of.  radium  are  the  seat  of  a  continuous 
development  of  heat  which  maintains  them  at  a  temperature  con- 
siderably in  their  experiments  (1*5°  C.)  above  that  of  the  surrounding 
heat.  They  found  that  the  heat  produced  by  1  gramme  of  radium 
per  hour  is  about  100  calories. 

The  existence  of  the  a  radiation  has  been  beautifully  shown  by 
Sir  William  Crookes  by  the  following  method :  a  small  piece  of  a  salt 
of  radium  is  placed  close  to  a  screen  of  zinc  blende ;  on  examining  the 
screen  in  a  dark  room  by  a  lens  it  is  seen  to  be  dotted  over  with 
scintillating  phosphorescent  patches  which  are  continually  changing 
their  places,  these  patches  mark  the  spots  where  the  screen  is  struck  by 
the  positively  electrified  a  rays. 


SUPPLEMENTARY   NOTES.  553 

CHAPTER  XII.,  p.  322. 

More  recent  experiments  made  by  Debierne  indicate  that  actinium 
is  a  distinct  substance,  as  it  has  been  found  to  give  out  an  emanation 
whose  activity  lasts  only  for  a  few  seconds ;  the  induced  radio-activity 
due  to  actinium  is  said  to  die  away  rather  more  slowly  than  that  due 
to  radium. 

As  the  duration  of  the  activity  of  a  radio-active  substance  is  the 
property  by  which  it  is  most  easily  recognised  it  may  be  useful  to  give 
a  table  of  the  time  taken  for  the  activity  to  fall  to  half  its  value  for 
those  cases  in  which  it  has  been  determined. 

Time  taken  for  activity  to  fall  to  half  its  value. 

Thorium  emanation,  1  minute. 

Induced  activity  due  to  thorium,  1 1  hours. 

Radium  emanation,  4  days. 

Induced  activity  due  to  radium,  28  minutes. 

Actinium  emanation,  a  few  seconds. 

Induced  activity  due  to  actinium,  rather  less  than  28  minutes. 

Radio-active  gas  from  water,  4  days. 

Induced  radio-activity  due  to  this  gas,  about  40  minutes. 

Induced  radio-activity  on  a  negatively 

electrified  wire  in  the  open  air,         about  40  minutes. 

The  Curies  have  found  that  when  bodies  have  been  exposed  for 
a  long  time  to  the  radium  emanation  there  is  in  addition  to  the  radio- 
activity which  disappears  in  28  minutes  a  small  residual  activity 
which  takes  months  to  disappear. 

CHAPTER  XII.,  p.  326*. 

Experiments  recently  made  at  the  Cavendish  Laboratory  have 
shown  that  by  far  the  greater  part  of  the  conductivity  produced,  by 
bubbling  air  through  water  is  due  to  the  presence  in  the  water  of 
a  radio-active  gas.  The  amount  of  this  gas  varies  much  in  different 
samples  of  water,  in  fresh  deep  well  water  from  many  parts  of 
England  I  have  found  it  in  considerable  .quantity,  while  there  is  very 
little  in  surface  or  rain  water.  This  gas  is  liberated  when  air  is 
bubbled  through  the  water,  it  can  also  be  obtained  by  boiling  the 
water,  the  gas  expelled  from  water  by  boiling  having  very  high 
conductivity.  When  once  the  gas  has  been  drawn  out  of  the  water, 
subsequent  boiling  or  bubbling  produces  very  little  conducting  gas. 

35—5 


554  SUPPLEMENTARY  NOTES. 

Mr  Adams  in  some  experiments  made  at  the  Cavendish  Laboratory 
found  that  water  after  a  rest  of  about  a  week  recovered  to  some 
extent  its  power  of  giving  off  a  radio-active  gas,  the  maximum 
recovery  amounting  to  about  10°/0  of  the  gas  initially  present.  The 
independent  existence  of  this  gas  was  shown  in  the  following  way: 
a  large  quantity  of  highly  conducting  gas  was  liquefied  at  the  Royal 
Institution  by  Professor  Dewar,  the  liquid  so  obtained  was  allowed 
to  evaporate  and  the  gas  coming  off  at  the  beginning  of  the  evapora- 
tion and  also  at  the  very  end  when  it  was  nearly  completed  collected 
and  tested,  the  gas  coming  off  at  the  beginning  was  found  to  have 
far  less  conductivity  than  the  gas  had  before  liquefaction  while  the 
gas  left  over  at  the  end  had  about  30  times  the  original  conductivity. 
The  conductivity  can  also  be  taken  out  of  the  gas  by  passing  it  slowly 
through  a  tube  immersed  in  liquid  air.  The  radio-active  gas  resembles 
very  closely  the  emanation  from  radium;  its  activity  has  been  shown 
by  Mr  Adams  to  fall  to  one-half  its  original  value  in  four  days,  the 
time  taken  for  the  same  process  in  the  radium  emanation,  the  induced 
radio-activity  due  to  the  gas  from  water  dies  away  to  half  its  value 
in  about  42  minutes,  the  same  as  that  of  a  negatively  electrified  wire 
in  air;  according  to  Curie  the  time  taken  for  the  induced  activity 
due  to  the  radium  emanation  to  fall  to  half  its  value  is  28  minutes. 
I  have  also  found  that  if  to  water  from  which  the  gas  has  been 
expelled,  certain  substances,  notably  finely  powdered  bricks,  the  blue 
clay  from  the  Cambridge  gault,  or  garden  soil,  are  added,  radio-active 
gas  is  again  obtained  by  boiling  or  bubbling.  I  have  not  however  by 
such  means  been  able  to  get  anything  like  the  quantity  of  gas  there  is 
in  Cambridge  tap-water. 


CHAPTER  XVIIL,  p.  525. 

Blondlot  has  shown  that  the  rays  which  affect  the  sparks  in  the 
experiment  described  on  p.  525  are  not  Rontgen  rays  but  a  new  type 
of  ray  which  he  calls  N  rays,  these  rays  are  emitted  by  incandescent 
burners  as  well  as  by  sparks,  they  are  refracted  and  are  apparently  of- 
very  long  wave,  some  measured  by  Sagnac  had  a  wave-length  of  ]-  of  a 
millimetre.  The  rays  when  they  fall  upon  incandescent  platinum 
increase  its  brightness  without  apparently  increasing  appreciably  the 
average  temperature  of  the  glowing  wire. 


INDEX. 


The  numbers  refer  to  the  pages. 


a  rays  275 

Absorption  of  cathode  rays  310 
of  polonium  rays  321 
of  radium  rays  307,  311 
of  Eontgen  rays  249,  253 
of  light,   connection    between   and 

photoelectric  effects  217,  218 
Actinium  294,  322 
Additive  property,  absorption  of  Rdnt- 

gen  rays  an  253 
ionization    produced    by    Eontgen 

rays  an  248 

cathode  fall  of  potential  an  442 
minimum  spark  potential  an  443 
After-glow  in  gases  498 
Aitken,  effect  of  dust  on  clouds  135,  179 
Alkali  metals,  conductivity  of  salts  of  199 
effect  of  cathode  rays  on  salts  of  495 
photoelectric  effects  of  212 
Allen,  H.  S.,  ions  produced  by  secondary 

Eontgen  radiation  265 
Allen  and  Eutherford,  rate  of  escape  of 

electricity  through  air  5 
decay  of  induced  radio-activity  323 
Almy,  discharge  from  fine  wire  408,  410 
effect  of  magnetic  force  on  discharge 

476 
Alternating  current,  discharge  of  from 

point  405 

through  gas  at  very  low  pressures  477 
Anode  fall  of  potential  458 
Arc,  electric  416  et  seq. 
appearance  of  417 
distribution  of  potential  difference 

between  terminals  422 
exploring  electrodes  in  423 
effect  of  pressure  on  potential  dif- 
ference 420 
hissing  430 
intermittence  of  419 
magnetic  field  effect  on  431 
potential  difference  in  different  gases 

421 
potential   difference  at  anode  and 

cathode  422 
relation  between  potential  difference 


Arc,  electric,  current  and  length  of  arc 

417  et  seq. 
temperature  of  416 
theory  of  424 
with  terminals  of  different  metals 

419 
Arons,    potential    difference   of  arc   in 

different  gases  421 
relation  between  potential  difference 

and  current  in  arc  418 
Arrhenius,  conductivity  of  flames  197, 

200 

electrical  wind  403 
Aurora  Borealis  165 
Atmospheric  electricity  3 
Atomic  weight  of  radium  306 
Aurora  Borealis  165 
Austin  and  Starke,  reflection  of  cathode 

rays  504 
velocity  of  reflected  cathode  rays 

507 
Ayrton,  Mrs,  appearance  of  electric  arc 

417 

hissing  arc  430 
potential  drop  at  anode  422 
Ayrton,  W.  E.,  relation  between  current 
and   potential  difference  in    arc 
418 

/S  rays  275 

Bailie,  spark  potential  352 

discharge   in   a  non-uniform  field 

387 
Baker,  effect  of  moisture  on  chemical 

combination  142 
Baly,  striated  discharge  463 
Baly  and  Eamsay,  critical  pressure  in 

oxygen  447 

Barkla,  secondary  Rontgen  rays  551 
Barus,  electrification  of  a  steam  jet  133 
electrical  conductivity  due  to  phos- 
phorus 324 

Battelli,  critical  pressure  in  oxygen  447 
Becquerel,  conductivity  of  hot  air  155 
electric  deflection  of  rays  from  ra- 
dium 111,  308 


556 


INDEX. 


Becquerel,  magnetic  deflection  of  rays 
from  radium  307 

uranium  282 
rays  274  et  seq. 
radiation  from  uranium  274 
ratio  of  charge  to  mass  for  negative 

ions  from  radium  111 
separation   of   radio-active    consti- 
tuent from  uranium  284 
Bedwell,  electricity  conductivity  due  to 

phosphorus  324 

Bemont,  discovery  of  radium  304 
Benoist,  ionisation  of  gas  by  Kontgen 

rays  246 

absorption  of  Kontgen  rays  251 
Berliner,  gases  from  incandescent  solids 

179 
Birkeland,  effect  of  magnetic  force  on 

discharge  476 
magnetic  spectrum  of  cathode  rays 

513 
Bloudel,  arc  with  terminals  of  different 

metals  419 

Blondlot,  conductivity  of  hot  air  155 
velocity  of  propagation  of  Kontgen 

rays  525 
N  rays  554 
Blythe,  distribution  of  potential  in  spark 

discharge  390 

Blythswood  (Lord),  reflection  of  Kont- 
gen rays  524 

Bohr,  critical  pressure  in  oxygen  447 
Bouty,  spark  potential  352 

connection  between  electric  strength 

and  pressure  372 

Boys,  leakage  of  electricity  through  air  2 
Branly,  electrification   by  incandescent 

solids  158,  181 

Braun,  electrification  by  flames  196    ' 
ionization  in  explosive  wave  194 
Breisig,  photoelectric  effects  in  different 

gases  230 

Brooks  (Miss),  heat  produced  in  sparks  396 
and  Kutherford,  molecular  weight 

of  radium  emanation  318 
Brunhes,  velocity  of  Kontgen  rays  525 
Bubbling  through  water,  electrification 

due  to  334 
Buisson,  effect  of  ultra-violet  light  on 

air  140 

photoelectric  effect  in  gases  214 
velocity  of    negative    ions    due  to 
ultra-violet  light  221 

Cady,  thermal  effects   due   to   cathode 

rays  500 
Campbell- Swinton,  hollowness  of  pencil 

of  cathode  rays  517 
path  of  cathode  rays  515 
production  of  Bontgen  rays  525 
phosphorescence  under  cathode  rays 

495 
reflection  of  cathode  rays  504 


Canalstrahlen  117,  519 

magnetic  deflection  of  520 
positive  charge  carried  by  521 
oxidation  by  520 

Cantor,  relation  of  oxidation  to  photo- 
electric effects  242 

Capstick,  cathode  fall  of  potential  441 
Carey-Foster    and    Pryson,    connection 
between  spark  potential  and  spark 
length  356 

Carr,  spark  potential  352,  357,  360,  361 
effect  of  material  of  electrodes  on 

spark  353 

Cathode,  current  density  at  443 
disintegration  of  451 
distribution  of  potential  near  444 
fall  of  potential  439 

depends  on  nature  of  cathode 

440,  442. 

effect  of  current  on  446 
Cathode  rays  493  et  seq. 
absorption  of  310 
from  uranium  282 
ionisation  due  to  312 
effect  on  salts  of  alkali  metals  495 
reducing  action  of  496 
mechanical  effects  due  to  501 
thermal  effects  due  to  499 
electric  charge  carried  by  502 
mass  of  corpuscles  in  91  et  seq. 
reflection  of  503 
magnetic  spectrum  of  513 
scattering  of  512 
transmission  of  510 
velocity  of  reflected  507 
velocity  after? transmission  512 
repulsion  of  streams  of  517 
determination  of  e/m  for  91  et  seq. 
Cavallo,     ionisation     by    incandescent 

solids  155  . 

Charge,  electric,  carried  by  an  ion,  de- 
termination of  121  et  seq. 
electric,  on  ions  56 
determination    of   ratio   of   charge 
to  mass  of  negative  ion  at  low 
pressures  91  et  seq. 

for  corpuscles   emitted  by  ra- 
dium 111 
Chattock,  velocities  of  ions  from  point 

discharge  53,  399 

Chemical  action,  effect  of  on  steam  jet  134 
electrification  due  to  336 
effects  produced  by  radium  320 
Canalstrahlen  520 
cathode  rays  496 
Child,    potential    gradient    in    ionized 

gas  61 

Chrystal,  connection  between  spark  po- 
tential and  spark  length  356 
Clouds  produced  by  chemical  action  134 
formed  round  ions  124 
relative   efficiency  of  positive  and 
negative  in  producing  145 


INDEX. 


557 


Clouds  produced  by  gases  liberated  by 

electrolysis  337 
Collie  and  Kara  say,  discharge  through 

helium  365 

Collision,  ionisation  by  230 
Cohesion  dielcctrique  372 
Coloration    of    salts    of   alkali   metals 

produced  by  cathode  rays  495 
Colson,  nuclei  from  metals  142 
Condensation  round  negative  ion  124 
Condensation  round  ions  136 
Conduction  of  electricity  through  air  1 

et  seq. 

Conductivity  of  gases,  properties  of  9 
removed  by  filtering  10 

electric  field  11 
various  ways  of  producing  8 
relation    between   current   and 
potential   differences    12,  64 
et  seq. 

air  1  et  seq. 

air  in  caves  and  cellars  7 
air  increases  with   time  at  first 

in  a  closed  vessel  6' 
Conductivity  of  flames  197 

produced  by  bubbling  through  water 

326 

Constitution  of  sparks  396 
Constriction   in  tube,  effect  of  on  dis- 
charge 466,  490 

Cook,  actinic  power  of  spark  discharge  411 
Corpuscles  131 

from  hot  wires  164 

given    out    by   metals    exposed    to 

ultra-violet  light  241 
given  out  by  radium  309 
in  motion  ionise  a  gas  339 
Coulier,  effect  of  dust  on  clouds  135 
Coulomb,  leakage  of  electricity  through 

air  1 
Critical  spark  length  356 

pressure  for  spark  discharge  361 
Crookes  (Sir  W.),  insulation  of  a  good 

vacuum  5 

radiation  from  uranium  283 
dark  space  377,  432,  444 
disintegration  of  cathode  451 
striations  463 
cathode  rays  494 
phosphorescence  under  cathode  rays 

495 
mechanical  effects  due  to  cathode 

rays  501 

repulsion  of  cathodic  streams  518 
radiation  from  radium  552 
Curie,  M.  and  Mme,  discovery  of  radium 

303 

atomic  weight  of  radium  306 
activity  of  radium  306 
character  of  radium  radiation  307 
negative  corpuscles   given   out   by 

radium  111,  308 
radio-active  gas  from  radium  318 


Curie,    M.   and    Mme,    induced    radio- 
activity due  to  radium  316 
ionisation  due  to  uranium  ionisa- 
tion 281 

Curie,  Mme,  discovers  polonium  320 
absorption  of  rays  from  polonium 

320 
Curie,  Mme  and  Laborde,  temperature 

of  radium  in  air  552 
Curie,   effect   of  radium  rays  on   con- 
ductivity of  liquids  524^ 
Curie  and  Sagnac,  negative  electricity 
given  out   by  plates  exposed  to 
Kontgen  rays  266 

Current,     connection     with     potential 
difference  for  discharge  through 
a  gas  12,  72 
saturation  12 

Current,  variation  of,  with  potential 
difference  for  leak  due  to  ultra- 
violet light  219 

connection  between,  and  spark  po- 
tential for  point  discharge  401 
current  density  at  cathode  443 
effect   of,   on   cathode,   fall  of 

potential  446 
Currents,  air  caused  by  motion  of  ions  58 

Dark  space,  Crookes'  377,  432,  444 
thickness  of  446 

connection  with  mean  free  path 
of  molecules  of  the  gas  450 
relation  of  to  current  450 
theory  of  481 
Faraday's  433 

Debierne,  actinium  294,  322 
Demarcay,  spectrum  of  radium  305 
Des  Coudres,  velocity  of  cathode  rays 
103 

after      transmission      through 

metal   plates   512 

Dewar,  heat  produced  by  spark  395 
Diffraction  of  Rontgen  rays  528 
Diffusion  of  ions  20 
coefficients  of  27 
of  gases  30 

Discharge  from  points  399 
Discharge,  electric,  through  gas  at  low 

pressure  432  et  seq. 
theory  of  479  et  seq. 
Discharge,  striations  in  463 
Disintegration  of  cathode  451 
Distance  between  striations  463 
Dorn,  negative  ions  given  out  by  plate 

exposed  to  Kontgen  rays  266 
velocity  of  corpuscles  in  secondary 

Rontgen  radiation  268 
effect  of  moisture  on  thorium  289 
persistence  of   radiation    from   ra- 
dium 317 

Drops,  electrification  of  143 
Duddell  and  Marchant,  arc  with  termi- 
nals of  different  metals  419 


558 


INDEX. 


Dufay,  ionisation  by  incandescent  solids 

155 
Duncan,  Bowland,  and  Todd,  effect  of 

pressure  on   potential  difference 

in  the  arc  420 
Durack,  ionisation   by  rapidly  moving 

corpuscles  343 

Duration  of  conductivity  of  gases  9, 16, 18 
Dust,  effect  of  on  rate  of  leak  through 


on  rate  of  recombination  of  ions  18 
on  clouds  135 

Du   Tour,   ionisation   by    incandescent 
solids  155 

Earhart,  spark  potential  for  very  short 

sparks  352,  384 

Ebert,  thickness  of  dark  space  446 
Ebert    and   E.    Wiedemann,    effect    of 
ultra-violet  light  on  sparks  348 
thermal  effects  due  to  cathode  rays 

499 
discharge  at  low  pressures  by  rapidly 

alternating  currents  477 
repulsion  of  cathode  streams  519 
Edison  effect  162 

Edlund,  relation  between  potential  dif- 
ference and  current  in  arc  dis- 
charge 418 
Eichberg  and  Kallir,  arc  with  terminals 

of  different  metals  419 
Electric  field,  effect  of  on  conductivity 

of  gases  11 

force,  distribution  of,  in  discharge 
434 

in  Faraday  dark  space  453 

positive  column  455 
Electric  discharge  through  gases  at  low 

pressures  432 
theory  of  479  et  seq. 
Electrical  wind,  403 
Electricity,  one  fluid  theory  of  131 
effect  of  on  steam  jet  133,  134 
Electrification     of    gases    liberated    by 

electrolysis  337 
due  to  bubbling  through  water  334 

chemical  action  336 
effect  of  on  induced  radio-activity 

322 
effect  of  on  condensation  of  drops 

149 

Electrodeless  discharge  used  to  find  con- 
ductivity of  flames  173 
glow  produced  by  447 
effect  of  magnetic  force  on  475 
Electrolysis,  charge  on  gas  liberated  by 

337 

Electrolytic  gas,  clouds  produced  by  337 
Elster  and  Geitel,  leakage  of  electricity 
through  open  air  3 

air  in  caves  and  cellars  7 
ionic   theory  of   atmospheric   elec- 
tricity 149 


Elster  and  Geitel,  ionisation  by  incan- 
descent solids  156  et  seq. 
gases  from  incandescent  solids  179 
effect  of  magnet  on  leak  from  hot 

wire  186 
photoelectric  effects  211,  218 

effect  of  plane  of  polarisation 
on  234 

temperature  on  238 
induced  radio-activity  on  negatively 

electrified  wire  322,  328 
radio-activity  of  air  absorbed  in  the 

ground  546 
Emanation  from  thorium  285 

source  of  290 
Emanation  from  radium  316 

density  of  318 

Energy  in  Rontgen  rays  280 
Enright,   electrification   from    chemical 

action  336 

Entladungstrahlen  491 
Erman,  electrification  by  flames  196 
Ewers,  thermal  effects  due  to  cathode 

rays  499 
positive    charge  carried  by   Canal- 

strahlen  521 

Exner  and  Haschek,  pressure  in  sparks 
394 

Faraday,  influence  of  successive  sparks 

347 

dissymmetry  of  discharge  391 
dark  space  433,  453 
Filtering,  effect  of  on  conduction  through 

gases  10 

Flames,  source  of  ionisation  in  172 
conductivity  of  193 
velocity  of  ions  in  203 
ionisation  in  gases  from  193 
distribution  of  electrification  in  191 
effect  of  electric  field  on  195 
Fleming,  Edison  effect  162 

exploding  electrode  in  arc  423 
theory  of  arc  423 
Fluid  theory  of  electricity  131 
Fluorescence,  connection  of  with  photo- 
electric effects  242 

Fomm,  diffraction  of  Kontgen  rays  528 
Force,   electric   distribution  of  in  dis- 
charge tube  434 

in  positive  column  455 
in  Faraday  dark  space  453 
Foster,  Carey-,  connection  between  spark 

potential  and  spark  length  356 
Free-path,    connection  of  with  critical 

spark  length  372,  374 
with  electric  force  in  discharge  379, 

383 

thickness  of  dark  space  450 
Frohlich,    relation     between    potential 
difference  and  current  in  arc  417 

Gait,  electrification  due  to  bubbling  335 


INDEX. 


559 


Gases,    rates   of   normal   leak  through 

different  gases  6 

given  out  by  incandescent  solids  179 
photoelectric  properties  of  213 
Gehrcke,   velocity  of  reflected   cathode 

rays  507 
Geitel,  rate  of  leak  from  a  charged  body 

in  air  4 

Geitel  and  Elster,  see  Elster  and  Geitel 
Giese,    electrification    by   flames,    193, 

197 
Giesel,  luminosity  of  radium,  306 

magnetic  deflection  of  radium  rays 

307 
Goldstein,    effect    of    temperature    on 

cathode  fall  of  potential  440 
distance  between  striations  463 
effect   of    constriction    in  tube   on 
discharge  466 

magnetic  force  on  striations  473 
similarity   between    striations   and 

effects  at  cathode  487 
cathode  rays  493 

effect    of    on    salts    of    alkali 

metals  495 
reflection  of  504 
phosphorescent    patterns    pro- 
duced by  515 

repulsion  of  cathodic  streams    517 
Canalstrahlen  520 

Graham,  distribution  of  electric   force 
in  discharge  tube  434 
near  cathode  445 
in  Faraday  dark  space  453 
positive  column  455 
Granqvist,  disintegration  of  cathode  451 
Grier  and  Rutherford,   radiation   from 

uranium  283 

Gross  and  Shephard,  relation  between 
potential  difference  and  current 
in  arc  418 

Guthrie,  ionisation  by  incandescent 
solids  155 

Haga  and  Wind,  diffraction  of  Bontgen 
rays  528 

Hall-effect  in  gases  205  et  seq. 
in  discharge  tube  461 

Hallwachs,  photoelectric  effects  210,  217 

Hankel,  electrification  by  flames  196 

Hardy,  chemical  effects  due  to  Kontgen 
rays  552 

Harmuzescu,  ionisation  of  gases  by 
Eontgen  rays  246 

Harvey  and  Hird,  discharge  of  alter- 
nating current  from  a  point  405 

Haschek  and  Mache,  pressure  in  spark 

394 
and  Exner,  pressure  in  spark  394 

Heat  produced  by  spark  395 

Heat,  effect  of  on  cathode  fall  of  potential 
440 

Helium,  spark  potential  in  364 


Helium,  discharge  through  365 

viscosity  of  366 
Helmholtz  (K.  von),  effect  of  electricity 

on  a  steam  jet  133 
and  Eicharz,  electrification  of  steam 
jet  134 

formation  of  clouds  by  chemi- 
cal action  134 
Hemsalech   and   Schuster,  constitution 

of  sparks  396 
Henry,  phosphorescence  of  sulphide  of 

zinc  274 
Henry  (J.),  photoelectric  effect  of  gases 

214 
Hertz,  photoelectric  effects  211 

effect  of  ultra-violet  light  on  spark 

348 

explosive  wave  in  spark  394 
penetration  of  thin  metal  by  cathode 

rays  494,  509 

Herwig,  electrification  by  flames  196 
Herz,  distribution   of  electric  force  in 

discharge  434 

in  the  positive  column  455 
Heydwiller,  heat  produced  by  sparks  395 
Himstedt,  discharge  of  alternating  cur- 
rent from  a  point  405 
alternating  currents  through  gases 

at  low  pressures  477 
Hird   and  Harvey,   discharge   of  alter- 
nating current  from  a  point  405 
Hissing  arc  430 
Hittorf,  leakage  of  electricity  through 

air  2 
effect  of  salts   on  conductivity  of 

flames  177 

electrification  by  flames  196 
difficulty  of  producing  short  sparks 

359 
distribution  of  electric  force  in  arc 

434 

cathode  full  of  potential  439,  440 
electric  force  in  Faraday  dark  space 
453 

positive  column  455 
temperature  in  discharge  tube  468 
action  of  magnet  on  distribution  of 

glow  over  cathode  472 
cathode  rays  493 

Hoffmann,  Entladungstrahlen  49° 
Holmgren,    electrification    by    shaking 

wet  cloth  143 

Holtz,  electrification  by  flames  195 
Hoor,  photoelectric  effects  211 

influence  of  temperature  on  238 
Humphreys,  effect  of  pressure  on  spec- 
trum 395 

Impurities  in  gas,  effect  of  on  point  dis- 
charge 402 

Incandescent  solids,  ratio  of  charge  to 
mass  of  corpuscles  produced  by 
111 


560 


INDEX. 


Incandescent  solids,  ratio  of  charge  to 
mass  for  positive  ions  produced 
by  119 

ionisation  by  155  et  seq. 
corpuscles  emitted  by  164 
positive  ions  produced  by  171 
gases  given  out  by  179 
Induced    radio-activity    from    thorium  • 
emanation  294 

duration  of  296 
time  taken  to  produce  297 
penetrating  power  of  299 
due  to  radium  316 
on  negatively  electrified  wires  in  air 
322,  328 

rate  of  decay  of  323 
Intermittence  of  arc  discharge '419 
Ionisation  by   incandescent  solids  155 

et  seq. 

by  collision  230,'  339  et  seq. 
by  Eontgen  rays  246 

variation  of  with  temperature 
255 

pressure  246 
in  different  gases  247 

an  additive  property  248 
by  cathode  rays  312,  339 
by  Lenard  rays  340 
by  uranium   rays  in   different 

gas  278,  281 
by  radium  rays  in  different  gas 

312 
by  polonium  rays   in  different 

gas  312 

by  ultra-violet  light  312 
in  explosive  wave  214 
Ions  11 

explain  conductivity  of  gases  13 
theory  of  conduction  through  air 

by  15 

rate  of  recombination  of  18 
rate  of  diffusion  of  20 
velocity  of  32-56 
difference  of  velocities  of  positive 

and  negative  37  et  seq. 
velocity  of  in  flames  49,  176 
salt  vapours  203 
point  discharge  53 
charge  on  56,  121  et  seq. 
mathematical  theory  of  conduction 

by  64 

motion  of  in  magnetic  field  79-90 
motion  of  under  both  electric  and 

magnetic  forces  86 
ratio  of  mass  to  charge  for  negative 
in  cathode  rays  91,  95,  99, 100, 102 
ratio  of  mass  to  charge  for  negative 
produced  by  ultra-violet  light  107 
incandescent  wire  111 
radio-active  substances  111,  112 
positive  ratio  of  charge  to  mass  117 

given  out  by  radium  282 
positive  produced  by  hot  wire  171 


Ions,  work  required  to  produce  189, 190, 
255 

condensation  round  125 

number  of,  produced  by  secondary 
Eontgen  radiation  265 

negative  given  out  by  metals  ex- 
posed to  Eontgen  rays  266 

number  of  in  various  parts  of  dis- 
charge 460 

Jaumann,  effect  of  rapid  variations  in 
potential  on  spark  350 

Johnson,  effect  of  rapid  variations  in 
potential  on  spark  352 

Kallir  and  Eichberg,  arc  with  terminals 

of  different  metals  419 
Kaufmann,  ratio  of  mass  to  charge  of 

ion  100 

heat  produced  by  discharge  395 
scattering  of  cathode  rays  512 
effect  of  velocity  on  mass  of  cor- 
puscle 533 
Kelvin  (Lord),  electrification  by  shaking 

mercury  143 

effect  of  surface  tension  on  forma- 
tion of  clouds  149 
negative  electrification  due  to  bub- 
bling 217,  334,   335 
spark  potential  352 
Kiessling,   effect  of  dust  on  clouds  135 
Kirby    and    Townsend,    ionisation    by 

collision  341 

Knoblauch,  photoelectric  effects  213 
relation  of  oxidation  to  242 
Koch,  ionisation  produced  by  hot  wires 

172 
Kosters,  electrification  due  to  bubbling 

335,  337 

Kreusler,  photoelectric  current  through 
gases  223 

Lag  of  electric  spark  348  et  seq. 
Lang,  v.,  relation  between  potential  dif- 
ference and  current  in  arc  418 
Langevin,  recombination  of  ions  547 
velocity  of  ions  548 
work  required  to  ionise  a  gas  551 
secondary  Eontgen  rays  551 
Laplace,  electrification  due  to  chemical 

action  336 

Larmor,  radiation  from  an  ion  543 
Lavoiser,  electrification  due  to  chemical 

action  336 
Leakage  of  electricity  through  air  1  et  seq. 

in  closed  vessels  6 
Lecher,  intermittence  of  arc  419 
Lehmann,  appearance  of  short  sparks  358 
effect  of  constriction  on  discharge 

466 

action  of  magnet  on  discharge  472 
similarity  between    striations   and 
effects  at  the  cathode  487 


INDEX. 


561 


Leithausers,  velocity  of  cathode  rays 
after  transmission  through  metals 
512 

Lenard,  ratio  of  mass  to  charge  of  ion 
in  Lenard  rays  95,  96 

when  produced  by  ultra-violet 

light  109 
effect  of  ultra-violet  light  on  oases 

140 

electrification  by  splashing  143,  334 
photoelectric  effects  in  gases  214 
effect  of  pressure  on  photoelectric 

leak  224 

absorption  of  Lenard  rays  310 
transmission  of  cathode  rays  510 
rays  510 
Lenard   and  Wolff,   clouds   formed   by 

ultra-violet  light  135 
Length  of   spark,  relation  of  to  spark 

potential  354 

Liebig,  spark  potential,  352,  355 
Linss,    leakage    of    electricity   through 

air  3 

Luggin,  relation  between  potential  dif- 
ference and  current  in  arc  419 
potential  drop  at  anode  and  cathode 

in  arc  discharge  422 
Lyman,  cathode  fall  of  potential  440 

McClean,  electrification  due  to  bubbling 

through  water  335 
McClelland,  velocity  of  ions  in  flames 

49,  194 
ions  produced  by  incandescent  wires 

158 

current  through  hot  gases  185 
McClelland  and  J.  J.  Thomson,  absorp- 
tion of  Eontgen  rays  245 
McClennan,  ionisation  produced  by  cath- 
ode rays  312 
discharge  produced  by  bodies  after 

exposure  to  cathode  rays  499 
effect  of  walls  of  vessel  on  leak  545 
existence  of  penetrating  radiation 

545 
McClung,  effect  of  pressure  on  rate  of 

recombination  of  ions  19 
effect  of  temperature  on  the  rate  of 

recombination  of  ions  550 
effect  of  temperature  on  the  ionisa- 
tion of  a  gas  551 
McCluug  and  Rutherford,  absorption  of 

Rontgen  rays  251 
energy  in  Eontgen  rays  280 
Mache  and  Haschek,  pressure  in  spark 

394 

Magna,  heat  produced  by  electric  dis- 
charge 395 

Magnetic  deflection  of  rays  from  ura- 
nium 282 

radium  307 

Magnetic  field,  effect  of  on  leak  from 
hot  wire  186 


Magnetic  field,  effect  of  on  lag  of  spark 
350 

spark  397 

arc  431 

discharge  in  vacuum  tubes 

4V70 
on  distribution  of  glow  on 

cathode  472 
on  negative  glow  470 
on  striations  473 
motion  of  ions  79 
theory  of  effect  on  discharge  489 
spectrum  of  cathode  rays  513 
Marchant  and  Duddell,  arc  with  termi- 
nals of  different  metals  419 
Marx,   distribution  of   temperature  in 
discharge  through  hot  gases  205 
transverse     velocity     of     ions     in 

magnetic  field  205 
Mass  of  a  corpuscle  131 

effect  of  velocity  on  532 
Matteucci,  leakage  of  electricity  through 

air  2 

conductivity  due  to  phosphorus  324 
Meissner,  formation  of  clouds  134,  338 

pressure  in  spark  393 
Merritt,    velocity  •  of   reflected   cathode 

rays  507 
Metals,  nuclei  from  142 

non-arcing  420 

Mey,  cathode  fall  of  potential  440,  442 
Meyer    and    Schweidler,    magnetic    de- 
flection of  radium  rays  307 
Minimum  potential  for  point  discharge 
399 

spark  discharge  366 
Mohler,  pressure  in  spark  394 
Moisture,  effect  of,  on  thorium  radiation 
289 

sparks  347 
lag  of  sparks  350 
cathode  fall  440 
Molecular  weight  of  radium  emanation 

318 

Molecules,   number   of  in  cubic   centi- 
metre of  gas  57,  130 
Motion  of  ion  under  magnetic  force  79 

and  electric  forces  86 
Moulton    and    Spottiswoode,    effect    of 
magnetic  force  on  striatiom  473 
similarity  between  effects  at  cathode 

and  striations  487 

Miiller  and  De  la  Eue,  effect  of  nature 
of  electrodes  on  spark  potential 
353 
discharge  between  pointed  electrodes 

389 

dissymmetry  of  discharge  391 
pressure  in  spark  393 
striated  discharge  433,  463 

Nabl,  effect  of  pressure  on  rate  of  re- 
combination of  ions  19 


562 


INDEX. 


Naccari,  conductivity  due  to  phosphorus 

324 
heat  produced  by  sparks  395 

Naccari  and  Bellati,  heat  produced  by 
sparks  395 

Nahrwold,  leakage  of  electricity  through 

air  2 
gases  from  incandescent  solids  179 

Narr,  leakage  of  electricity  through  air  2 

Natterer,  spark  length  in  different  gases 
375 

Nebel,  relation  between  potential  differ- 
ence and  current  in  arc  418 

Neesen  and  Paalzow,  effect  of  magnetic 
field  on  discharge  474 

Negative  electrification,  induced  radio- 
activity caused  by  322 

Negative  ions,  velocity  of  37 

condensation  round  121-125,  129 

Negative  glow  433 

action  of  magnet  on  470 

Neureneuf,  electrification  in  flames  195 

Newall,  electrodeless  discharge  447 
after-glow  in  gases  498 

Nitrogen,  spark  potential  in  364 

Non-arcing  metals  420 

Number  of  molecules  in  a  cubic  centi- 
metre of  gas  57,  130 

Obermayer,  discharge  from  a  point  411 
Orgler,  spark  potential  352 
Owen,  formation  of  clouds  180 
Owens,  radio-activity  of  thorium  284 
Oxidation  by  Canalstrahlen  520 

connection    of    with    photoelectric 
effects  242 

Paalzow,  heat  produced  by  spark  395 
Paalzow  and  Neesen,  effect  of  magnetic 

force  on  discharge  474 
Paschen,  spark  potential  352 

discharge  in  a  non-uniform  field  387 
Paschen's  law  367  et  seq. 
Patterson,  variation  of  leak  in  a  closed 

vessel  with  pressure  545 
Peace,    potential    required   to    produce 

sparks  352 
effect  of  material  of  electrode  on 

spark  potential  353 

Perrin,  effect  of  pressure  on  ionisation 
by  Rontgen  rays  246 

temperature   on  ionisation   by 

Kontgen  rays  255 
ionisation    of    different    gases    by 

Kontgen  rays  247 
secondary  Kontgen  radiation  259 
electric  charge  carried  by  cathode 

rays  502 
Pettinelli  and  Marolli,  discharge  from 

hot  electrodes  192 

Peukert,  relation  between  potential  dif- 
ference and  current  in  the  arc 
418 


Phosphorescence  274 

caused  by  cathode  rays  494 
Phosphorus,  conductivity  due  to  324 
Photoelectric  effects  211  et  seq. 
duration  of  242 
influence  of  temperature  on  238 
influence  of  plane  of  polarisa- 
tion on  234 

connection    with    phosphores- 
cence and  ionisation  242 
connection  with  oxidation  242 
properties  of  gases  213 
Pliicker,  action  of  magnet  on  discharge 

470 
Poggendorff,   heat    produced   by   spark 

395 
Point  discharge,  velocity  of  ions  from 

53,  399 
connection  between  spark  potential 

and  current  401,  408 
effect  of  impurities  on  402 
with  alternating  currents  405 
theory  of  406 
Polarisation  of  light,  effect  of  plane  of 

on  photoelectric  effects  234 
Polonium  304,  320 

absorption  of  radiation  from  321 
Positive  column  433 

effect  of  magnet  on  472 
Positive  ions,  velocity  of  37 

ratio  of  charge  to  mass  117 
near  hot  wire  171 
from  ultra-violet  light  214 
from  radium  282 
rays  519 

Potential,  distribution  of  in  spark  dis- 
charge 390 

minimum  spark  potential  366 
cathode  fall  of  439 
anode  fall  of  458 
Pouillet,  electrification  by  flames  195 

chemical  action  336 
Precht,  effect  of  magnetic  force  on  spark 

398 
point  discharge  400 

with  alternating  current  405 
Precht  and  Runge,  atomic  weight  of  ra- 
dium 306 

Preece  (Sir  W.),  Edison  effect  162 
Pressure,  effect  of,  on  leak  through  air  5 
on  rate  of  recombination  of  ions 

19 

ultra-violet  light  discharge  226 
spark  potential  360  et  seq. 
potential  difference  in  arc  420 
potential  gradient  in   positive 

column  456 
in  spark  392 
Priestley,    ionisation    by    incandescent 

solids  155 

Pringsheim,  relation  between  current 
and  potential  difference  in  an 
ionised  gas  75 


INDEX. 


563 


Pringsheim,  effect  of  moisture  on  chemi- 
cal combination  142 
discharge  through  hot  gases  178 

Radiation   a   and  ft   from    radio-active 

substance  275 
Radiation  from  an  ion  543 
Radio-active  emanations  285,  316,  318 
Radio-active  gas  in  water  553 
Radio-activity  of  uranium  275 
thorium  284 
radium  303 
polonium  304 
actinium  304 
induced  294 
duration  of  296 
time  taken  to  develop  297 
penetrating  power  of  299 
Radium,  positive  ions  given  out  by  282 
discovery  of  303  et  seq. 
spectrum  of  305 
atomic  weight  of  306 
types  of  radiation  given  out  by  307, 

308 

radiation,  absorption  of  311 
persistence  of  emanation  316 
effect  of  heat  on  317 
chemical  effects  produced  by  320 
radiation,  effect  of  on  liquids  524 
temperature  of  in  air  552 
Rain,  radio-activity  of  546 
Ramsay  and  Baly,  critical  pressure  of 

oxygen  447 
Ramsay  and  Collie,  discharge  through 

helium  365 

Ratio  of  charge  to  mass  for  corpuscles 
91  et  seq. 

positive  ions  117,  119 
Ratio  of  velocities  of  positive  and  nega- 
tive ions  37-41 
Rayleigh  (Lord),  viscosity  of  helium  366 

critical  pressure  of  oxygen  447 
Recombination  of  ions  14 
rate  of  16,  547 

affected  by  dust  18 
Reflection  of  cathode  rays  503 

Rontgen  rays  524 
Reinold  and  Riicker  on  surface  tension 

152 

Reiss,  heat  produced  by  sparks  395 
Repulsion  of  cathode  rays  517 
Richardson,   ionisation  from  incandes- 
cent solids  161 

Richarz  and  Helmholtz,  effect  of  elec- 
trification and  chemical  action  on 
a  steam  jet  133,  134 
Righi,  photoelectric  effects  211 

effect  of  temperature  on  238 
ionisation    of    gases    by     Rontgen 

rays  246 
effect   of  material  of  electrode  on 

spark  potential  353 
Rollman,  heat  produced  by  spark  395 


Rontgen  rays  244,  523  et  seq. 
absorption  of  245,~249,  253 
ionisation  of  gases  by  246 

effects    of   pressure   and  tem- 
perature on  246,  255 
effect  on  steam  jet  135 

clouds  135 
secondary  258  et  seq. 

in  air  260 
tertiary  273 
reflection  of  524 
source  of  524 
theory  of 
velocity  of  525 
diffraction  of  528 
effect  on  solids  and  liquids  524 
Rontgen,  v.,  connection  between  electric 
strength  and  mean  free  path  374 
point  discharge  399 
Rood,  reflection  of  Rontgen  rays  324 
Rowland,  Duncan,  and  Todd,  effect  of 
pressure  on  potential   difference 
in  arc  discharge  420    ts 
Rue,  De  la  and  Miiller,  effect  of  material 
of  electrode  on  spark  potential  353 
sparks  between  pointed  electrodes 

389 
dissymmetry  of  electric    discharge 

391 

pressure  in  sparks  393 
striated  discharge  433,  463 
Runge   and   Precht,   atomic   weight   of 

radium  306 

Russell,  nuclei  from  metals  142 
Rutherford,  velocity  of  ions  32,  36,  47,  50 
current     from    incandescent    wire 

175,  185 
ionisation    of   different    gases    by 

Rontgen  rays  247 
absorption  of  Rontgen  rays  249 
on  uranium  radiation  275 
ionisation   due  to  uranium  radia- 
tion 281 
positive  ions  given  out  by  radium 

282 

radio-activity  of  thorium  284 
emanation  from  thorium  285 
effect  of  temperature  on  radiation 

from  thorium  288 
induced  radio-activity  from  thox  um 
294 

properties  of  297 
penetrating  power  of  297 
velocity  of  positive  ions  producing 

induced  radio-activity  300 
persistence  of  radiation  from  radium 

317 
effect  of  heat  on  radium  radiation 

317 
existence  of  penetrating  radiation 

545 

Rutherford  and  Allen,  rate  of  leak  of 
electricity  through  air  5 


564 


INDEX. 


Kutkerford  and  Miss  Brooks,  molecular 

weight  of  radium  emanation  318 

Eutherford  and  Cooke,  effect  of  walls 

of  vessel  on  leak  545 
Eutherford  and  Grier,  uranium  radia- 
tion 283 

Butherford   and    McClung,   absorption 
of  Bontgen  rays  251 

energy  in  Etmtgen  rays  280 
Eutherford  and  Soddy,  effect  of  moisture 

on  thorium  emanation  289 
source  of  thorium  radiation  290 
origin  of  ratio-activity  552 

Sagnac,  secondary  Eontgen  rays  259 

tertiary  Eontgen  rays  273 
Sagnac  and  Curie,  negative  ions  given 
out  by  plate  exposed  to  Eontgen 
rays  266 
Salt  vapours,  conductivity  of  200  et  seq. 

maximum  current  carried  by  210 
Saturation  current  12 
Scattering  of  cathode  rays  512 
Schmidt,  photoelectric  effects  213 

relation  of  fluorescence  and  ionisa- 
tion  to  photoelectric  effects  242 
radio-activity  of  thorium  284 
oxidation  by  Canalstrahlen  520 
Schmidt  and  E.  Wiedemann,  coloration 

produced  by  cathode  rays  496 
Schuster,  ratio  of  charge  to  mass  of  an 

ion  99 

shadow  thrown  on  cathode  383 
discharge  in  a  non-uniform  field  387 
thickness  of  Crookes  dark  space  433 
distribution  of  potential  near  cath- 
ode 444 

influence  of  current  on  dark  space  450 
action  of  magnet  on  distribution  of 

glow  over  cathode  472 
Schuster  and   Hemsalech,  constitution 

of  sparks  396 

Schweidler,  v. ,  current  and  potential  dif- 
ference curve  12 

discharge  by  ultra-violet  light  221 
effect  of  pressure  on  224,  233 
Schweidler    and    Meyer,    magnetic    de- 
flection of  radium  radiation  307 
Secondary  Eontgen  rays  258 

theory  of  268 

Seitz,  transmission  of  cathode  rays  511 
Shadow  on  cathode  383 
Shephard  and  Gross,  relation  between 
potential  difference  and  current 
in  arc  418 

Sieveking,  point  discharge  401 
Simon,  ratio  of  charge  to  mass  of  cor- 
puscle 100 

Skinner,    distribution   of  electric  force 
along  discharge  434 
near  cathode  445 
in  Faraday  dark  space  453 
anode  fall  of  potential  458 


Smithells,  Dawson,  and  Wilson,    con- 
ductivity of  salt  vapours  200 
Soddy   and  Eutherford,  effect  of  tem- 
perature on  thorium  radiation  289 
source  of  radio-activity  290 
Sommerfeld,  diffraction  of  Eontgen  rays 

539 

Source  of  Eontgen  rays  524 
Spark  discharge  346  et  seq. 
effect  of  moisture  of  347 
lag  of  348 

influence  of  ultra-violet  light  on  348 
effect  of  rapid  changes  in  potential 

on  351 

theory  of  376 
Spark  length,  critical  356 
Spark  potential  352  et  seq. 

effect  of  material  of  electrode  on  353 
connection  with  spark  length   354 
et  seq. 

pressure  360  et  seq. 
minimum  366 
in  a  non-uniform  field  387 
tables  of  412 
Sparks,  pressure  in  392 
heat  produced  by  395 
constitution  of  396 
very  short.  384 

effect  of  magnetic  field  on  397 
Spectrum  of  radium  305 
Spottiswoode    and    Moulton,    effect   of 

magnetic  force  on  striation  473 
similarity   between    striations   and 

effects  at  cathode  487 
Stark,  cathode  fall  of  potential  446 

work  required  to  ionise  a  gas  551 
Starke,  reflection  of  cathode  rays  504 
Starke  and  Austin,  reflection  of  cathode 

rays  504 

Steam  jet,  effect  of  electricity  on  133 
incandescent  wire  on  134 
chemical  action  on  134 
Eontgen  rays  on  135 
Stewart,  gases  from  incandescent  solids 

179 
Stokes  (Sir  G.  G.),  motion  of  an  ion  in 

magnetic  field  82 
velocity  of  falling  drop  121 
theory  of  Eontgen  rays  539 
Stoletow,  photoelectric  effects  211,  217 
connection    between    current    and 
potential  difference  for  leak  caused 
by  ultra-violet  light  219 
effect  of  pressure  on  photoelectric 
leak  225,  232 

temperature    on    photoelectric 

leak  238 
Strachan,  distribution  of  electric  force 

in  discharge  436 

Straight    line    radiations    from    radio- 
active bodies  289 
Striations  433,  463 

distance  between  463 


INDEX. 


565 


Striations,  effect  of  size  of  discharge  tube 
and  pressure  on  distance  between 
465 
effect    of   nature    of    gas    on    465 

magnetic  force  on  473 
in  gas  at  high  pressures  468 
Strutt  (Hon.  E.  J.),  absorption  of  radium 

rays  311 
spark  potential  352 

in  different  gases  364 
cathode  fall  of  potential  441 
magnetic  spectrum  of  cathode  rays 

514 

effect  of  walls  of  vessel  on  leak  545 
Surface  tension,  Remold  and  Eiicker  on 

152 
Swyngedauw,  effect  of  ultra-violet  light 

on  sparks  348 

effect    of  rate  of    variation  of  po- 
tential on  spark  discharge  352 

Tables  of  spark  potential  412 
Tamm,  point  discharge  400-401 
Temperature,    influence   of    on    photo- 
electric effects  238 

iouisation  by  Eontgen  rays  255, 

551 

thorium  radiation  288 
of  terminals  in  arc  416 
distribution   of  along   line   of  dis- 
charge through  gas  at  low  pres- 
sures 468 

Tertiary  Eontgen  radiation  273 
Theory    of    discharge     by    ultra-violet 

light  228 

secondary  radiation  268 
spark  discharge  376 
point  discharge  406 
arc  discharge  424 
discharge  through  gas  at  low  pres- 
sures 479  et  seq. 
Thermoluminescence  496 
Thorium,  radio-activity  of  284 

radiation,  effect  of  temperature  on  288 

moisture  on  289 
source  of  290 

Todd,  Eowland,   and  Duncan,  effect  of 
pressure  on  potential  difference 
in  arc  discharge  420 
Topler,  striations  at  high  pressures  468 
Townsend,   current   and   potential   dif- 
ference curve  12 
rate  of  recombination  of  ions  19 

diffusion  of  ions  25 
formation  of  clouds  134 
secondary  Eontgen  radiation  261 
electrification  due  to  chemical  action 

336 

charge  on  gas  liberated  by  electro- 
lysis 337 

velocity  of  ions  produced  by  chemi- 
cal action  338 
ionisation  by  collision  341 


Transparency  to  Eontgen   rays,  coeffi- 
cients of  252 
cathode  rays  313 
radium  rays  313 

Ultra-violet  light,  ratio  of  charge  to  mass 

for  corpuscle  produced  by  107 
effect  of  on  condensation  of  clouds 
139,  216 

on  air  140 

positive  ions  produced  by  214 
theory   of    discharge    due    to    228 

et  seq. 

effect  of,  on  lag  of  spark  349 
Uranium,  radiation  from  275 
ionisation  produced  by  281 
radio-active  constituent  of  283 

Vacuum,  insulation  of  5 
Varley,  relation  between  potential  dif- 
ference and  current  for  conduc- 
tion  caused  by  ultra-violet  light 
226 

Varley,  Cromwell,  cathode  rays  494 
Velocity  of  ions  31  et  seq. 

methods  of  measuring  34 
difference  between  positive  and 

negative  ions  37 
ratio  of  73 
table  of  60 
in  point  discharge  53 
in  salt  vapours  176/ 
in  Games  192     ^f 
cathode  rays  103j|<^ 
Eontgen  rays  525 
secondary  Eontgen  rays  268 
rays  from  uranium  282 
positive     ions    producing    induced 

ratio- activity  300 
corpuscles,    effect    of   on    ionizing 

power  344 
Villard,  reducing  action  of  cathode  rays 

496 
electrification  due  to  Canalstrahleu 

521 

Villari,  heat  produced  by  discharge  395 
Violle,  temperature  of  arc  416 

Walter,    discharge    before    passage    of 

spark  350 
Warburg,  leakage  of  electricity  through 

air  2 
lag  of  the  spark  348 

effect  of  ultra-violet  light   on 
349 

moisture  on  350 
magnetic  force  on  350 
effect  of  impurities  on  point  dis- 
charge 403 

cathode  fall  of  potential  439,  440 
Water,  conductivity  due  to  326 
electrification  due  to  334 
radio-active  gas  in  553 


566 


INDEX. 


Watson,    ionisation    by    incandescent 

solids  155 

Waves  in  air  produced  by  sparks  393 
Wehnelt,  shadow  cast  on  cathode  118 
discharge  from  cathode  443 
distribution  of  potential  near  cath- 
ode 445 
influence  of  current  on   thickness 

of  dark  space  451 
Wesendonck,  dissymmetry  of  discharge 

391 
Wiechert,  ratio  of  charge   to   mass   of 

an  ion  102 

Wiedemann    (E.),    temperature    of  gas 
conveying  electric  discharge  468 
constricted  discharge  477 
Entladungstrahlen  491 
thermoluminescence  496 
thermal  effects  due  to  cathode  rays 

499 

energy  required  to  produce   phos- 
phorescence 501 

Wiedemann  (E.)  and  Ebert,  discharge 
at  low  pressures  by  rapidly  alter- 
nating current  477 
thermal    effects    due    to    cathode 

rays.  499 

repulsion  of  cathode  streams  519 
effect  of  ultra-violet  light  on  spark 

348 

Wiedemann  (E.),   and  Schmidt,    color- 
ation produced  by  cathode  rays 
496 
Wiedemann    (G.),    heat    produced    by 

sparks  395 
Wien,    ratio    of    charge    to    mass    for 

positive  ion  117 
Canalstrahlen  520 

Willows,  distance  between  striations  463 
effect  of  size  of  discharge  tube  on 

stria  465 
influence  of  nature  of  gas  on  striae 

465 
effect  of  magnetic  field  on  discharge 

475 

Wilson,  C.  T.  E.,  leakage  of  electricity 

through  air  and  other  gases  4,  6 

condensation  of  clouds  round  ions 

121,  125,  136 
nuclei  from  metals  142 


Wilson,  C.  T.  E.,  relative  efficiency  of 
positive  and  negative  ions  in  pro- 
ducing clouds  145 
ions   produced  by  point  discharge 

411 

radio-activity  of  rain  546 
Wilson,  H.  A.,  ratio  of  mass  to  charge 

on  corpuscle  102 

effect  of  dissolved  salt  on  forma- 
tion of  clouds  141,  337 
source  of  ionisation  in  flames  172 
velocity  of  ions  in  salt  vapours  176 
discharge  through  flame  gases  178 
work  required  to  ionise  a  gas  190 
distribution  of  potential  in  hot  gases 

191 

velocity  of  ions  in  flames*192,  202 
conductivity  of  flames  197 
current  through  salt  vapours  201, 

210 

distribution  of  electric  force  in  dis- 
charge 434 

current  density  at  cathode  443 
electric  force  in  Faraday  dark  space 
453 

positive  column  455 
distribution  of  ions  along  discharge 

459 

Hall  effect  in  gases  461 
charge  on  the  ion  550 
effect  of  hydrogen  on  leak  from  hot 

wires  550 

Wind,  electrical  403 
Wind  and  Haga,  diffraction  of  Eontgen 

rays  528 
Wolf,    relation    of   spark   potential    to 

pressure  371 
Wood,"distribution  of  temperature  along 

line  of  discharge  469 
Work  required  to  ionise  a  gas  190,  255, 

551 
Wurtz,  non-arcing  metals  420 

Zeleny,  velocity  of  positive  and  negative 

ions  37-47        ^- 
currents  in  gas  caused  by  motion 

of  ions  59 

potential  gradient  in  ionised  gas  61 
effect    of    temperature    on    photo- 
electric effects  238 


CAMBRIDGE:   PRINTED  BY  J.  AND  c.  F.  CLAY,  AT  THE  UNIVERSITY  PRESS 


Ofej    ^  v        9 


14  DAY  USE 

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